Indie (adj): abbreviated form of independent - referring to a fad that would hate to be called popular, but that's exactly what it is.
Indie movies (or indie kids would probably call them "films"): Movies without a happy ending. Or, perhaps more commonly, movies without any conclusion for an end.
Indie music: the music that all the kids who think they're cool claimed "they discovered." Bands that make EPs because they can't come up w/a whole album. Bands whose tours include basement bars and if they're lucky, one late night show appearance. I'm sure your friend's cousin's friend knows their drummer, or at least claims to.
Indie kids: claim to be different, but all have the same black hair, track jackets, and CDs. They go to the same concerts and do the same head bobbing and occasional closed eyes swaying. Need to buy their clothes a size larger than they do now.
What's in a name? Irony of all ironies.