To my mind, it would be inaccurate to claim that the 16th and 17th centuries saw the rise of nation-states, though there may have been some fringe cases preempting what was to come. You could potentially make the case that emerging economic interconnectivity in those centuries formalized a sort of proto-statehood. However, according to historian C.A. Bayly in 2004, “historians and theorists of nationalism do not find economic explanations for the rise of national sentiment as convincing as they once did.”
Most historians are likely to argue that the rise of nation-states is a phenomenon that sort of begins in the exact bisection of the nineteenth century, in the wake of the Revolutions of 1848, and plays out globally in the ensuing decades. Brian Porter-Szuchs, for example, states “[i]t probably wouldn’t be an exaggeration to say that the generation born in the 1860s witnessed more profound changes than any other in European history.” However, it should be noted that different countries adopted changes and reforms at different rates.
Prior to the emergence of nation-states, the specific boundaries between various countries was much less clear than they are today. Whereas today you could lay down and declare that your appendages are occupying four different states simultaneously, this would be an abstract idea indeed to most people in the eighteenth century. That isn’t to say that borders didn’t exist, but what exactly did they facilitate?
Take for example the case of Poland. Poland’s theoretical boundaries waxed and waned over many centuries, sometimes including, sometimes excluding, Lithuanians and/or Ukranians, and this meant… probably nothing to the vast majority of its peoples. Around the turn of the nineteenth century, nearly three-quarters of the population of Poland consisted of mere serfs, whose existence probably wasn’t at all concerned with much outside the community and the whims of the landowners.
As a result, the power structures under which a man could find himself were often overlapping, complex, and maybe even a bit confusing. According to Dominic Lieven's Nicholas II, by 1897, still only 44% of the Russian Tsar's subjects were "Russian." Why? Well, in the process of implementing the nation-state model, if the Tsar tried to play his hand too aggressively in very remote territories -- territories which did technically fall under his domain under the nation-state global arrangement -- he risked drawing the umbrage of the actual leaders or statesmen who more or less oversaw and administrated over the regions, who then might decide to take their ball (allegiances owed, for example) and go home (unilaterally change the terms of an arrangement, say). Authority, then, was less centralized prior to the rise of nation-states. During one period where Russia technically had sovereignty over Poland, an official policy to introduce the Russian language and church to the neighboring kingdom did not get very far. Who would administer this decree? Certainly a dynamic that was destined to change.
Returning to the aformentioned subjects of the Tsar, if some of them weren’t exactly "Russian," well, what were they? That's one of the questions the nation-state model of society hoped to answer. When Napoleon conquered much of Europe, one of his early answers to this question was to organize life around race and ethnicity -- but what exactly might that entail?
At first, one might imagine that's an arrangement we have today, or one that's been implemented extensively, right? The French are the French, the Germans the Germans, and the Poles are Polish. Right?
Well, not exactly. Remember the changing borders discussed earlier? The nation of Poland repeatedly changed in size to envelop the neighboring Lithuanians or Ukranians. So what exactly was a Pole anyway? Take the example of poet Adam Mickiewicz (1798-1855). His fatherland was technically Lithuania, though today his birthplace is technically Belarus. And the language he wrote and spoke was Polish. Today he is regarded as the national poet of all three: Poland, Lithuania, and Belarus. So, ethnically he is Lithuanian? Polish? “Slavic?” Of course an arbitrary convention could be enacted, but in any event Napoleon was ultimately not to have his way. But, more of Napoleon in a moment.
So, prior to the emergence of nation-states, if race and ethnicity were a flawed approach, how could a group of people be defined? And what about an ethnically heterogenous group, such as the population of today’s United States or the historical Moorish Spain? Perhaps... a common language?
Well, you probably get it by now: not so much. Without a centralized government overseeing education, regional languages played a much more important role than we might say they do today. Brits spoke Gaelic, Irish, Manx, Welsh, and Cornish, among others. In France, a third of its population did not speak the language we are thinking of today when we say, "parlez-vous français?"
So, going back, Napoleon’s emergence played a key role in necessitating some of the systems that would lead to the development of the nation-state. And not just because of the Napoleonic Code’s insistence on clearly-defined, written, accessible laws, which was an appealing paradigm when compared to the mélange of unofficial customs, subjugation to local landlords, etc., that one might be subject to otherwise.
Here’s the long and short of it: the Napoleonic Wars demanded such a mobilisation of the populace of Europe (in terms of the myriad resources required to staff and support larger and more professional armies) that its leaders simply had to adopt nation-state-style ideas in response. What kind of ideas are nestled inside the concept of statehood that would help marshall a state’s resources?
To name three, census-taking, surveying, and taxing. How can a king truly muster his forces -- and how can five coalitions coordinate -- if he doesn’t know the assets of his own kingdom (including its natural resources), or its number of able-bodied men? How can he finance a war without the appropriate revenue?
However, these thrusts towards statehood ended up being a bit of a flash in the pan, and largely deflated after the French conqueror had been defeated for good.
I won’t go into detail on the Revolutions of 1848 (as I have already spent a bit more time than I had intended in answering this question), but suffice to say they set the stage for what was to come. Think radical uprisings of intelligentsias, artisans, nationalists, in both major urban centers as well as rural. Governments were overthrown, at least 50 countries were affected by these uncoordinated efforts. The historical roots of the importance of “national identification” can be traced back to this so-called Springtime of the Peoples, which left in its wake an increasing desire for border control. You can imagine why. Statehood and national identification allowed for governments to distinguish between who and who-did-not belong to a given state, further expressed through the ability to deport persons of trouble back to their country of origin (not to mention the capability of holding that state culpable for the actions of these provocateurs).
The subsequent period between 1850-70 forged the ideas generated in the first half of the century alongside rapid industrialization, new weapons of war, and did so while stoked by the fires of nationalism. Thus, the modern nation-states were born. As we mentioned earlier, different nations developed at different speeds. Poland finally made the leap from a territory to a statehood in 1918 -- did this lumbering pace have anything to do with their difficulty in finding a national identity due to their historical shapeshifting?
I apologize for the very long-winded response, but now that I’ve written it I can’t bear to cut it down. However, here is a short list of things (edit: this list is not meant to be exhaustive or exclusive of other additions, but just represents some ideas we can be pretty sure of) we can identify with the development of statehood:
Sources:
As a potential follow up question: When considering the idea of nationalism as it pertains to the sixteenth-century nation-state, what separates sixteenth-century nationalism from the nationalism of today, or from that of the twentieth century? Does it relate to the view of an internal national identity vs an outward, colonial view of nation and expansion, or national protectionism?
This is a complex question, because historians, political theorists, international relations scholars, international law scholars, and political philosophers understand it differently. The easiest way to parse those differences is to identify which side of the dyad is emphasized in the answer: nation or state. I'll go with emphasis on "state."
"Nationalism" strikes me as a poor starting point for this discussion, for two reasons: (1) its meaning is overdetermined; and (2) nations are political fictions created by some combination of states and people, and so starting from the nation presupposes the distinction your question points to. Nevrtheless, most historians argue that modern political nationalism didn't take hold until the 19th century. That is not universal, however. Liah Greenfeld argues that nationalism originated in 15th century England, while other scholars like Susan Reynolds argue it's earlier still. These discussions are useful because they highlight different aspects of political organization that have endured or changed over time. However, when most people say "nationalism," they would likely emphasize its cultural rather than political dimensions.
I prefer Michel Foucault's line of thinking in his 77-78 lectures at the College de France, titled Security, Territory, Population. Foucault develops the history of what he calls "raison d'etat," or "reason of state," which is derived from Giovanni Botero's 1589 book Della Ragion di Stato. The key contribution of Botero, and I cannot remember if Foucault highlights this specifically or not, is the introduction of economics as a political (governing) category. At the risk of oversimplification, Foucault believed that thinking about politics from an economic standpoint required new systems of knowledge to allow the state to "see" the domain of its power differently. Let me explain by way of analogy.
"Economy" comes from the Greek oikonomia, or "household management." This heritage is acknowledged in analogies today, when politicians talk about national budgets as household budgets, for example. Now consider what the term "household" describes: it's a physical place (a building, some land) that is distinct from adjacent places (neighbors); it's a set of people to whom you have a particular legal and social relationship (family, other dependents, employees); and it's a set of responsibilities or concerns (providing food, for example). Foucault's argument, more or less, is that the state began to use a set of similar frameworks--territory, population, and security--to achieve something very similar to household management but on a much larger scale.
Foucault goes on to argue that the Treaty of Westphalia (1648) was the vehicle that propagated these ideas throughout Europe. A lot of ink has been spilled debunkning the Westphalian myth, especially with regard to "creation" of modern international sovereignty, and it does seem dubious to suggest that sovereignty didn't exist before the treaty. Nevertheless, Westphalia does provide concrete evidence that several of the cornerstone concepts underlying "reason of state" had taken hold in international relations and international law. Specifically, Westphalia acknowledges that territory is discrete, like the property lines between houses, and that the state's authority within its territory is exclusive and absolute. If Botero had provided some of the basic intellectual framework by which the state could begin to manage its object (the nation) from an economic perspective, Westphalia created the necessary international conditions for that transformation to take place in full. Thus, the "innovation" of Westphalia is the atomization of the international world.
One important consequence of this is that the state now knows what it's governing (more or less), and it can begin to pursue an agenda tailored to it. (In the household analogy, think of all the ambiguities that arise in shared housing situations like dorm rooms, and how those ambiguities resolve the more autonomy you have [dorm -> room -> apartment -> house -> land]) Now that the ground is cleared, the state can begin to manage what happens within its territory more directly. Economically this could involve things like regulating how much a grain producer could export to another country, and how much must be stored (this is an example Foucault uses). Or it might involve creating permit systems for merchants or transportation planning or even nationalizing/regularizing a language to streamline bureaucracy. The more work the state does in managing its territory and population (it's "nation"), the more closely the state and nation are sutured together.
From a purely economic standpoint, the homogeneity of the "nation" can be explained in part by the desire for efficient management. From a cultural standpoint, the homogeneity of the "nation" can be explained by the desire for a reproduction of the majority. I would add those two concepts--efficiency and majority--to Foucault's "security, territory, population" as the defining characteristics of the ideal modern nation-state.
Two things about this period guide my thinking about it, which I use philosophical writing as milestone markers for - philosophers are good at reflecting upon and condensing the "ideas in the air" at the time.
The first is the development of merchantalist philosophy over this time frame, which gradually outlined "national strategies" favoring trade over tributary methods of domination, and productivity economics over hoarding. Take for example, this quote from Discourse of the Common Weal of this Realm of England, 1549:
We must always take heed that we buy no more from strangers than we sell them, for so should we impoverish ourselves and enrich them.
This is a kind of justification for the emergence of colonial dynamics: keep the assets and liabilities on your national balance sheet balanced, and you will be wealthier. Acceptance of these ideas meant giving the merchant class what they want, which motivated demands for cheap, fungible labor(manifest in chattel slavery, impressment and indentures) and for nationalized projects and infrastructure, which in turn created the demand for expanded state bureaucracy to manage and enforce these ideas, and then for taxes and tarrifs to fund the state.
Although you could find parallels in, e.g. the Roman Empire, this precise dynamic was a new one, and supplemented by new technical knowledge that made larger trade markets available to seafarers, and a rise in printed materials and consequently literacy making technical specialties more widespread. Marco Polo made his journeys to Asia all the way back in the 1200's; and when Columbus made his expedition in 1492, it was in hopes of a new Asian route. With lower costs of trade, and more specialization, you get wealthier, more influential merchants, who lobby for their business, creating a positive feedback loop.
But of course, none of this happened all at once, and so it's a backdrop to the emergence of nation-states that you have this new prevaling economic dynamic which replaced manoralism.
By the time you reach Adam Smith's writing in the 18th century the notions of where wealth lies have progressed to a finer articulation of supply and demand, the uses of national currency, productivity, and other ideas still built on by present day economists, but you still have colonial dynamics in play that continue reverberating through history into the present day; the ACW, for one example, is often framed in terms of the South's colonial economy fighting the North's new industrial might.
Second, simultaneously, and especially later in this period, there are emerging trends in political philosophy towards something recognizable as modern liberal society. You have Hobbes, for example, with Leviathan(1651), who outlines a theory of social contracts. Locke describes separation of church and state in A Letter Concerning Toleration(1689). And so on, for a variety of topics around the role of states and the rights of individuals. These writings become influential to actual governance by the later 18th century - the U.S. Constitution, for one, incorporates many of these ideas.
The concept of the nation-state, in this context, emerges from a growing respect and critique for the political forces that states could wield, and advocacy for states to abide by rules that represent the nation, as opposed to its immediate rulers.