Prominence has to do with importance. If a band becomes famous, they've come into prominence.
Prominence is a type of importance: if you put a statue in the middle of a room, you're giving it a place of prominence. In movies, music, and sports, the most successful people have great prominence — they're prominent or famous. Anything that juts out or sticks out has prominence. Whether prominence comes from being widely known or just being hard to miss, you can't really ignore anything or anybody that has achieved prominence.