The joke was that “The Prince of Canada” had a revelation that branding yourself with attributes to make yourself popular was less important than what was on the inside of yourself. And then discovered that his wife was in fact empty on the inside, all she actually had was her brand.
(The Canadian Prince bit is relevant because on South Park all Canadians are depicted as having detached heads from their mouths up, unlike the Americans who are drawn with normal heads. It’s a running joke).