He is a huge white ghost cat, looking for a wife. The Ghost Cat lives in Maomoorin, a large legendary bell that he wears around his neck. He is constantly searching for a fiancee, and has a smaller version of his bell. Whoever holds this bell becomes his fiancee.
Originally Shampoo holds the smaller bell, but refuses to have anything to do with the Ghost Cat. After finding out that Ranma is her fiance, he decides to haunt Ranma.
Of course with Ranma's intense fear of cats this only makes him revert to using his Cat-fu on the Ghost Cat. Finally he sees that he is no match for Ranma and decides to look for a fiancee elsewhere.