The Chewbacca defense refers to any situation where nonsensical arguments are used to confuse the audience. More broadly, it can also refer to arguments where overwhelming quantities of data are presented as essential parts of the argument even though they are not, thus overwhelming the audience with information which cannot be successfully integrated and therefore cannot rationally be argued with.
The audience grows fatigued; many people will decide that they cannot understand the arguments because said arguments are too complicated for a non-expert, and therefore they are not qualified to criticize said arguments. At that point, it becomes necessary to either decide to trust the arguer to be making a rational case without trying to understand the data, or else to leave the dialog in order to seek better understanding of the argument (through more careful consideration of the data given and possibly through a search for additional sources).
Although Wikipedia claims this term originated with South Park, it seems likely that it refers to the scene in the original Star Wars movie (now Star Wars IV: A New Hope) in which C3PO is playing a board game with Chewbacca. C3PO objects to Chewbacca's technique for some perfectly good reason; Chewbacca emits a classic Wookiee roar, and Han Solo advises C3PO to "let the wookiee win", further explaining that it's not a good idea to get into an argument with anyone who can rip your arms out of your sockets. The "Chewbacca defense", then, if it is partly derived from this scene, includes both the incomprehensibility of the defense (the wookiee roar) and an element of threat due to overwhelming strength on the part of the defender.