What is a Pokemon event?

A Pokemon event can refer to different things. An official tournament can count as an official Pokemon event but more often it refers to a distribution of a (usually) rare Pokemon. This distribution can happen over WiFi or is held at a certain location where you can download it.
A Pokemon event is a once in a while event. Nintendo has an online event in which a person may receive special downloads or additional pokemon. This happens in both America and Japan.