The Butler's cat refers to the cat which is supposedly belongs and lives in the Butler household but has never actually been seen in the series. However there is evidence of it existence such as "The Used Combination" when Mabel Butler (the mother of Stan & Olive) accidentally trod in the Cat's food.
Many things about the cat is unknown such as its breed, its name or even where they got it from. It was most likely purchased from a pet store or they may have even had it from someone who could no longer have it. As for the breed it could either be a Tabby, Ginger, Persian, which are popular breeds.