Ultimately, audiophiles are most interested in getting the best sound possible. What's the best sound? There's the rub, it's completely subjective. Is "like they're playing in this very room" the best? Or is it studio level detail? It all depends on the person
One of the defining definitions IMO, is that audiophiles are mostly interested in the sound of their gear rather than the sound of the music (I'm sure I'd get flamed pretty hard on any audiophile site for saying that too)
There can be a "cliqueiness" to them too (vinyl fanatics, etc) and a whole lot of "you're listening wrong" mentality out there too, but I've probably found just as many easy going, non-judgemental folks too (probably because I just avoid the tribal, partsian elements all together)
From what I've gathered, for the most part musicians/studio pros don't consider themselves audiophiles