Purposely or not, bands tend to create personas along with their music. The persona is usually based on that of the lead singer or otherwise most conspicuous member, and musicians who find that their needs for self-expression don't jibe with their group's persona either quit for solo careers or set up side projects to which they can periodically retreat.
Under rare circumstances, you get bands that are essentially collections of these people. If it's a collection of people who are already famous, it's called a "supergroup." That, though, is a description that the members of The New Pornographers don't like, because the band is now a full-time gig and none of the groups they came from were famous.
Originally, the purpose was to have fun.