As in, how did international politics play out before the Thirty Years' War, and what changed?
Because, well, it for the first time gave people sovereignty and defined it. That's really it.
Some people, like my buddy /u/DonaldFDraper, don't even consider the Modern Era to begin at all until 1648 because, rightfully so at that, the entire 1500's - 1648 time was just a period starkly removed from modernity; it was defined by religious wars. Which provinces will worship which sect of Christianity, heresies, blah blah blah. 1648 changed all that because of religious toleration and from this, ideas of sovereignty arose. It really is the transition point between religious wars and political wars in the Western world as after this, well, they never happened again. Religious rivalries would, in short, be replaced by dynastic or political rivalries.
Most importantly of all though Westphalia neutered both the supremacy of the Emperor of the Holy Roman Empire and the spiritual universality of influence of the Pope. The Pope wouldn't be a diplomatic mediator anymore and the Holy Roman Emperor was not some centralized head of state over the Germanic states anymore; to be more blunt the state replaced the void where religion once filled ideas of motivations for war and for justification of rule. How did it go about this?
The Peace of Augsburg in 1555 would be recognized by all relevant parties, that is, all of Europe essentially. This means that every leader of any state can determine his/her own religion -- even if his liege supports another. This also included the very important caveat, the thing that really started this whole 30 Years' War mess, is that even if an official religion is declared by a state leader anyone can worship any denomination they wish publicly and without oppression. That is, religious oppression while still a cultural topic was no longer an issue of the state.
Sovereignty would be established. All states would have legal equality, states can no longer interfere with the internal affairs of another. These are called "Westphalian principles" and it means that, big to small, every state is equal and most importantly from that last bit the territorial integrity will be respected unless proper legal claims are presented.
So while sovereignty is never mentioned explicitly the principles of it were laid down here. We don't say we follow Westphalian sovereignty to a t or that it created it but that it laid the groundwork like you say. All the European major powers (Dutch, Spanish, Austrians, Swedish, French, etc.) all recognized territorial integrity, the internal affairs of foreign states are their own internal affairs, the state is responsible for the warlike actions of her own people (building political responsibility), and that everyone has the freedom to choose their own religious path (as long as it's Christian!). It neutered the power of the Pope and thus any ability for religious influence to really take hold of politics in a serious manner again and while, technically, "TECHNICALLY", Germanic states were still subservient to the Holy Roman Emperor (Hapsburgs/Austrians) it was de facto out at this point.
That's really the other super big issue -- the sovereignty of major powers like France and Spain had already been established by sheer force. That is it wasn't in a legalistic sense but they had such a big stick no one really messed with them anyways. However it would be Westphalia that gave legal equality/protection to the little guy.
With that said though we can not mistake this for some kind of intentional act of the signers/drafters of this treaty to create some kind of revolution to change concepts of sovereignty. This was a response to over a century of religious wars and being sick and freaking tired of it and it was sick of constant interference with states and interjections of major powers in small states business which just escalated small conflicts into major conflicts. It is the almost accidental extension of granting religious freedom, neutering the Emperor and Pope's powers, secularizing just about everything, and recognizing legal equality between states that these concepts arose which would mature over the next few hundred years.
The Thirty Years' War: Europe's Tragedy by Peter Wilson