An event is a pop-up during the game, that has an effect on anything from a single province, a nation to world politics. It is very similar to a decision and the only difference is that the player (or the AI) has control over decisions while events are somewhat random.
Events does usually have a set of parameters that need to be fulfilled in order for the event to happen. It can be anything e.g. a certain nation existing, a certain date passed, a certain invention or anything else. If these requirements are fulfilled, there is a mean time to happen (short: MTTH), which tells the average time for the event to fire in months.
Events can also happen as an effect of another nation taking a decision e.g. An Elephant for America? (decision).
Here you can find a list of events.
Mean Time to Happen
Mean time to happen (MTTH) is a concept used by the game's engine to determine how often events should occur. This is more useful than a probability, because a probability depends on how frequently an event is checked: if an event has the potential to fire every month, its probability must be a lot lower than if it can only fire every year, lest it fire much more often. An MTTH remains constant, however.
The probability of an event with a certain MTTH happening at a given moment is 1/MTTH. An event with an MTTH of 50 years has 1/50 = 0.02 chance of happening each year, for example, while an event with an MTTH of 200 days has a 1/200 = 0.005 chance of happening each day, assuming it has the potential to fire on any day.
How to mod an event
For a guide on how to mod in an event look at How to make an event.