To outwit means to be victorious over someone through means of thinking smarter than that person. You can find an example of it in the slogan for the American TV series Survivor "Outwit, Outplay, Outlast". Another example would be in a game of chess. If you won the game by making a move that the other player never even thought of then you have "outwitted" that person.

To out think someone. To be smarter, more clever.