When something is banned, it's illegal or not allowed. If you're wearing a banned t-shirt to school, it means there's a rule forbidding that particular kind of shirt.
You may have noticed "Banned Book Week" at your library or favorite bookstore — this is an occasion for book lovers to celebrate some of the excellent books that have been removed from schools and even town libraries over the years. Banned books are most often forbidden when a community member finds the subject matter personally objectionable or offensive. The Old English root is bannan, "to command or proclaim."