An indie band makes music on their own or on a very small record company, not with a large recording label. Your favorite indie group probably makes most of its money from touring, rather than by selling its music online.
Pop musicians who record songs independently of major labels are indie, and indie filmmakers work with small budgets and unknown actors, rather than large, well-funded film companies. The adjective is also sometimes used simply to mean "simple," "not commercial," or "outside of the mainstream." Indie, a shortened form of independent, has been around since about 1920, originally referring to movies, and by 1945 it was also used for music labels.