I always hear people say you can tell a lot about a person from the music they listen to. I think that's true, but it's also important to remember how they're perceiving said music. I know I listen to some music for the atmosphere, some music for the beautifully written lyrics, and some music because it's hilarious.
I find music can help with introspection as because, like most art, it's all about perception of the meaning. In art there is the creator's intended meaning and the audience's interpreted meaning. Both are important, but what is most important is the individual's perception of the piece. Listening to music we draw meaning from things based on our own experiences and feeling. Certain lyrics, certain sounds, certain waves are met with sensations, thoughts, and feelings. If one is looking to explore themselves all they need to do is listen to a little bit of music and express their opinion of it. All art is just symbols and symbols are structures given meaning by individuals. Therefore, individuals show a bit of their interpretation of the world through their interpretations of the symbols (sounds, lyrics, etc.) in music.
When people find their interpretations to be similar to the interpretations of others, they usually mesh well which is why people say you can learn a lot about a person from their music. You know if you mesh well with someone because you have the same thought process, you sync well together.
Now, keep in mind there is music for art and music for entertainment. Both are good, neither are bad, they just have a different purpose (and can sometimes bleed into each other). Art tries to express something, with symbols, entertainment does this but usually at the most basic level. I can't quite express the difference but you know it. What you're listening to there is meant to preoccupy your time not necessarily with deep feelings but feelings that are meant to keep your attention. It's a little bit like hypnotism, you already wanted to feel this way, it says, okay I can help you feel this way, and you accept. Most music does this but the emphasis is different depending on whether one is focusing more on art or entertainment. Great music can do both, but music that does one or the other isn't necessarily bad.
I love music, and I will always try to understand the art of symbolism, the interpretation of symbols, within music. Personally, for me, the purpose of music is introspection, and sharing that introspection with other people. It also serves as a way of altering one's emotions, or aiding one in understanding the emotions of others (in some instances). Either way most people seem to enjoy music. I've honestly only met one or two people who don't (some are just being contrary but there are people who legit just don't care for music). What matters most is why it matters anything at all to you.