The Chewbacca Defense is a joke about the legal process. It comes from an episode of the TV show South Park. In the episode, a character named Mr. Garrison has to go to court to face a charge. He decides to use a "Chewbacca Defense" which his lawyer explains as: "Your Honour, Chewbacca lives on Endor. Endor is a planet. The Defendant (Mr. Garrison) lives on Earth. Earth is not a planet. Therefore, Chewbacca is not the Defendant."
In other words, the Chewbacca Defense is a way of trying to prove you are not guilty by giving an argument that makes no sense and has nothing to do with the case. It's like trying to win a basketball game using a football. It's funny because it's so ridiculous, but it won't help you win in court!