“The Aristocrats” is a taboo-defying, off-color joke that has been told by numerous stand-up comedians and dates back to the vaudeville era.[1] It relates the story of a family trying to get an agent to book their stage act, which is remarkably vulgar and offensive. The punch line reveals that they incongruously bill themselves as “The Aristocrats”.[2]
That’s literally the point of the joke. Wiki link