Used when teasing another person. You want them to think you mean yes when really you mean no. Or vice versa. It's a great phrase to use, when asked a serious question, to lighten the mood. Or if you're already teasing, to win the battle and keep them guessing. It's also a good way to prevent the end of a conversation and begin a new, long one.
Guy- "Do you like me?"
Girl- "Maybeee maybe not."