A rather complex grand strategy game, you pick a country to control starting from the year 1444 all the way to 1821. There isn't any fixed objective to aim for: it's a good idea to try to get the achievements offered (such as world domination), as most are a real challenge to earn.
Each country is divided into provinces, allowing movement of you armies from one to another in real time - nothing here is turn based. Battles aren't controlled by you, as in total war: you make your army walk onto the same province as an opposing army, and the battle outcome is decided in part by random dice rolls, and in part by factors you can influence, such as generals, terrain, morale of troops. The same can be said for naval battles, where different types of ships behave differently depending on what sea province you are fighting in, if they are in the open ocean, or in a closed sea (such as the Mediterranean).
Diplomacy is fairly well fleshed out, countries can have a number of different governments, such as feudal monarchies or merchant republics, all that give different bonuses and maluses, and some (such as republics) offer the possibility to choose what type of leader you want, so as to give you more of a certain type of monarch points. You can offer alliances, royal marriages, support rebels, create false claims on provinces you don't own to give you a "casus belli" (a reason to go to war) among other things, the list is really really huge.
Monarch points are a "limiting factor" in the game, you have 3 different types of monarch points (Administrative, Diplomatic, Military), each that serve different purposes. For example, military points can be spent to buy a new general, or to treat a province harshly if rebels are likely to rise up there. (As of the Art of War update, rebel mechanics have changes slightly. Instead of each province possibly spawning rebels depending on a percentage, now each rebel faction has a counter that goes up or down depending on your country's stability and province modifiers, such as nationalism, culture or religion. Once the counter reaches 100%, multiple stacks of rebels spawn). Other points can be used to change your capital, annex vassals, gain provinces in peace deals, create buildings and much more. The gain of monarch points depend on your ruler, that can give from 0 points each to 6 point each month. By spending some of your income, you can also hire advisors, that can add to your monthly monarch points income, and grant you some nationwide bonuses.
Trade is also a large factor in the game, you have merchants and you can choose to send them to various trade nodes, and you can choose if you want them to try and collect money from that node with a malus, or to send the money that you collect upstream, to a different node where you can collect from. Having colonies and trade agreements with other countries helps your trade income, while being embargoed reduces your trade in nodes that the country embargoing you controls.
Paradox has created a lot of DLC for this game, but with each DLC comes a vast amount of free content as well, so it might be advisable to buy the base game before buying DLC, so as to see what you think about the game before commiting too much. If you choose to play online with a friend that owns the DLCs, even without owining the DLCs yourself, the game activates them, so its possible to try them out before you buy. It would also be a good idea to try and watch a tutorial beforehand (Arumba on youtube comes to mind), as the game doesn't do a great job of explaining all it has to offer.
It's a very time-consuming, and occasionaly frustrating game, but I found that the more I played it, the more I enjoyed it: I'm constantly learning new things I can use to my adantage, and the game is becoming more satisfying due to that.