A new act comes in to a vaudeville booker. It's a man, a woman, a little girl, and a little dog. They're all well dressed and clean-cut and wholesome looking.
"So what's your act?" the agent asks.
"It's kind of hard to describe", the man replies. "We'll show you."
So they start into a sweet little song-and-dance number. However, it starts to change. Soon is is the most ghastly, obscene routine imaginable. It's the kind of act that would be banned in Thailand.
(This is what makes this the World's Dirtiest Joke — it's all in your head. I'm sure you can think of things that would gross you out totally that I might consider a mildly boring kink, and vice versa. Just imagine the grossest thing you possibly can.)
As the act comes to a close, it changes back to a sweet little song-and-dance. They've worked cleaning themselves up and rearranging clothing into the act, so that when they finish, they're all clean-cut and wholesome looking again.
The agent is aghast. "Well, what do you think of it?" the man asks.
The agent is speechless. He tries to think of something to say, but all that comes out is "What do you call your act"?
The metaphor is obvious.