Something that's accepted is considered to be an established fact, or a correct idea. It's accepted among most university students that it's important to get a college degree.
While in the United States it's usual for men to wear pants rather than skirts, in Scotland kilts are an accepted clothing choice for men. The accepted way of doing anything depends a great deal on where you are and what group of people you're with, in fact. The adjective accepted comes from the verb accept, "consent to receive," which comes from the Latin acceptare, "take or receive willingly."