I'm so glad you asked :) Music is beautiful and genuine. It speaks to our emotions, but also teaches us about people, places, history, and events (this is culture). In studying song lyrics, you get a range of vocabulary, from familiar, everyday words to poetic and highly sophisticated language. Songs can be listened to over and over without getting old, so they are a great way to review after learning.
There is so much variety in music and it's always changing to reflect the people and society. English songs in particular have had enormous popularity around the world. They're referenced in movies, books, TV, even by other music artists. But, they're truly best when you understand what they mean. While I don't recommend learning English only through music, it's definitely a key part of becoming a well-rounded and fluent speaker.