[rolfea]

It really depends what time period you're referring to. Maybe broadly we could say that it's music that is either notably ahead of it's contemporaries in terms of innovation or that intentionally breaks out of stylistic models of its time to do something new.

So in those terms, Beethoven was at one point "avant-garde" in that his some of his compositions were so strikingly progressive compared to those of his contemporaries that they stood out. They were "at the front" of musical innovation in that sense.

John Cage started to compose music that intentionally and radically diverted from the trajectory of traditional western art music, so that was considered "avant-garde," although it was so influential, that I'd say much of it has become "canonized" in a way that performing it isn't really innovative of "edgy" in the way it was at it's original reception.

Today I think it's hard to pin down because there aren't really any established traditions that composers are breaking away from like they were at the cusp between the 19th and 20th centuries. I've seen and performed pieces for amplified fluorescent light bulbs, 4 screaming men in loin clothes, and for a solo performer articulating gestures in ASL to a pre-recorded musical track. None of it was scandalous, and some of it was quite good.