A music snob listens to more music than you. As a result they are able to make a better informed judgement on what music is best as they have listened to a wider spectrum of styles. They spend their spare time digging around for music that they perceive to be better than what has been spoon fed to them by the radio. This allows them to hear music that doesn't get credited by major media sources and so aids them in making a better judgement on what music is better.
Often dismissed by others as only liking music on the basis that it is obscure, skeptics of music snobs often choose to make this misinformed judgement because they don't understand the appeal of finding out about less mainstream music. In reality the music snob will prefer less mainstream music solely because it is more original and sounds better.
person 1: "you're such a music snob, you only like music because no one else has heard of it"
Music snob: "Actually I like the music I like because it sounds better and I have spend a lot of time and effort looking for music. It's like looking into a treasure chest. You will pick something from the top and say that it's fantastic, where as I will empty the entire chest, sift through everything and choose only the finest treasure. See what I mean?"