"Bae," if you don't know, is a slang word for boyfriend or girlfriend that became super-popular on Twitter early this year. Here is a Google trends graph.
(The height of the line prior to the major spike at the very end comes from people searching the acronym "BAE.")
Though "bae" rose to prominence thanks mostly to Twitter's black community, it has now thoroughly been co-opted by white people, which, duh, is why Zach Braff is finally hearing about it.
Of course, this could be even more hilarious: Zach Braff could think "bae" is a great word, in which case it might show up in one of his dumb movies.