I made a post on my blog in which I was trying to broadly outline events between the 1500s and the 1800s. At least, I was trying to offer my interpretation. It was most amateur; I really need to get back in the habit of citing my sources, and having them NOT ONLY being Wikipedia, but I digress.
I went over the circumstances which aided in the development of the Protestant Revolution, the colonisation of the Americas, the revolutions etc. in broad strokes.
But through all of this, I could find no reason to include the Italian Renaissance in the post. I know that the period is widely touted by historians as a time that changed everything, but I can't really get a grasp on what they mean.
These at least are how I understood the other major processes (I'm summarising even more than I did in the post, because I don't want this to be too long). Stop me at any time if I'm wrong.
European colonisation: Portugal desired means to expand its military and economic power, but was caught between Spain and Morocco. Around the same time, Infante Henrique the Navigator patronised the mass production of a new vessel called the Nau, which had ocean-going capabilities. This allowed Portugal to form island colonies that opened trade on a hitherto unknown scale. Other maritime nations followed suit to get a cut.
Protestantism: Invention of the printing press enabled ideas to be spread faster by making written documents cheaper to manufacture. Martin Luther copied and spread his words and managed to be the first denomination not to be systematically crushed by the Catholic Church. Later resulting wars broke the stranglehold Catholicism held on Europe, paving the way for a more religiously and ideologically pluralistic environment.
English Civil War: Power gradually accumulated in the hands of the nobility -starting from the early 13th century- and conflict with the king came to a head when Charles I started throwing his weight around. War was had, Charles got a little in over his head, and Parliament imposed their terms. The demands for responsible, representative government had a hand in influencing the development of the American Revolution.
French Revolution: Bankruptcy of the state following involvement in the American Revolution, famine, concentration of wealth in the hands of the clergy and other assorted mismanagement resulted in a lot of unhappy people. War was had and a lot of people got in over their heads. Napoleon stepped in and put an end to the buffoonery, crowned himself emperor, and I stopped after that.
The events and inventions leading up to all of these seem pretty clear to me, but when I looked up the Italian Renaissance, the most I could get out of it was 'A lot of pretty paintings and sculptures and buildings were made'.
Uh, that's great, but how does that impact government, society or infrastructure? I know Niccolo Machiavelli's Il Principe was released around that time, but did that have the same impact as Thomas Hobbes' Leviathan, for example?
Obviously I'm missing something here, but what is it?
Along with the Protestant Reformation as you correctly point out, the Italian Renaissance was absolutely fundamental in shaping the sorts of political thinking that we associate with modernity. Without the republicanism of the Renaissance, it's hard to imagine either the English Civil War or the French Revolution taking the forms that they eventually did -- or the various strands of enlightened, liberal, or radical thinking that emerged from them.
The Italian Renaissance saw the emergence of fundamental ideas like the state, conceiving of it for the first time in post-classical thought as something distinct from the person of the ruler (or rulers), and territorially limited rather than the unlimited "empire" and "res publica Christiana" of medieval political thought. Thus Giovanni Botero in 1589 could give his definition of "The State [as] a stable rule over a people", and concepts like the coup d'état which were unimaginable in medieval political thought became articulated and well-understood. (On the latter, see the very interesting, short article by Jens Bartelson, "Making Exceptions: Some Remarks on the Concept of the Coup d'état".)
It was in the Renaissance, in fact, that "politics" as we now understand it (re)emerged as something understood to be a distinct sphere of society, not just a form of moral philosophy. As Quentin Skinner says:
The first writer to think of himself with complete self-consciousness as a political scientist was Brunetto Latini, Dante's revered teacher ... [but] the genre ... may be said to culminate in Machiavelli's Prince. (Foundations of Modern Political Thought, vol. 2, p. 350.)
You can see this distinction between politics and morality very clearly in The Prince, which can still manage to shock a modern reader even though it's so deeply ingrained in our understanding of politics:
[I]t will be found that something which looks like virtue, if followed, would be [the prince's] ruin; whilst something else, which looks like vice, yet followed brings him security and prosperity. (The Prince, XV)
The best books on the subject of the influence of the Renaissance on political thought are still probably Quentin Skinner's The Foundations of Modern Political Thought (in 2 volumes) and J. G. A. Pocock's The Machiavellian Moment, and I would encourage you to have a look at both if you have the time.
Machiavelli's Il Principe was released around that time, but did that have the same impact as Thomas Hobbes' Leviathan, for example?
Machiavelli was enormously influential, and in fact there is a reasonably direct line leading from Machiavelli to English republicanism, and from there to American political thought (though the links with Hobbes specifically are a bit more obscure -- see David Wootton, 'Thomas Hobbes's Machiavellian Moments').