Events are changes in the game state that are made under the direction of special scripts that the game has. The scripting language includes the ability to pop up a dialog for the player's consideration, allowing multiple choices with different effects. For modders, event coding is the easiest and most accessible part of the game to modify. Many mods exist which add a variety of events to many countries which have few or no events in the vanilla version of the game.
There are two important subclasses of events in vanilla EU2. These are random events, which are recurrent and happen to all countries, and scripted events, which are country-specific and which occur only once (if that), typically at a fixed date or small fixed range of dates in each game. Scripted events are usually based on specific historical occurances, and there are very few of them (or none) for some countries.
It would be possible to have country-specific random events, but only one country (Nippon) has very many of these. (In addition, Mali and Sudan have specific events for changing their state religion.)