Notifications in the Facebook mobile app have been expanded to support friends' milestone (birthdays and such), sports scores and game start reminders based on the Pages you've liked, and events you've joined. These are customizable.
Disabled by default, you can also add support for local events and news, weather updates, local movies, and a list of places to eat. To do this, you must enable Location History.
The changes are rolling out gradually as of yesterday to iPhone and Android users in the US. Presumably, they'll hit the rest of the world in the coming weeks.