Funny-Bunny is a phrase meant to call someone an idiot in a simplistic way. Repeating the phrase over and over causes confusion and is a way to insult those that are not aware of the joke. The more they ask what a "Funny-Bunny" is, the greater the fool they are.
"You're such a Funny-Bunny!"
"What does that mean?"
"You just proved my point...Funny-Bunny"