I would say that it partially describes who you are. People certainly are influenced by their music, especially if it has words. I would say that it tells the person what kind of people influence them (artists/other 'rock dude' friends/etc). This is true especially if the person only listens to one kind of music. You can assume what some of the superficial qualities the person has are by their music, but you can't really judge that much under the surface about the person.
I listen to people such as Miles Davis and John Coltrane, I'm not sure how much that says about me.
That's my opinion anyway.