A celebrity is...

A celebrity is a person who is known for his well-knownness

This is another example of a definitional joke. The joke here seems to lie in the circular nature of the definition. Someone being known for being well known makes the listener wonder how they came to be well known in the first place.

This joke gently pokes fun at celebrities, since if the statement were made about top selling authors, major league baseball players, leaders of countries, or any other group of well known people, a explanation of why they came to be well known could be provided, but I personally couldn't come up with a reason why a generic celebrity deserves to be well known.