Well, it's difficult to explain why different artforms, in general, move us. It's not just music, of course. For others, it may be film, novels, poems, fashion, etc. At the end of day, these artforms are truly unique (and often beautiful) expressions of our creativity and imagination. We're drawn to the greatest artists and creative individuals probably because of 1) admiration and 2) we somehow relate to their works of art.

Paul Ekman is a psychologist famous for his research on body language/nonverbal communication. He found that there are at least several "universal" emotions and corresponding facial expressions, like anger, sadness, joy, disgust, etc. However, there are thousands of expressions our facial muscles can produce, and it's probable that we learn at least a few of them from our environments and cultures.