It is the part of a joke that is supposed to trigger laughter. For every good joke (in theory) there is a set-up and a punch line. A good set-up builds the joke up like blowing up a balloon and the punch line is like popping the balloon with a pin.
For example, SET-UP: "I asked my wife where she wants to go for our next vacation." She said, "Somewhere I've never been to before."
PUNCH LINE: I thought for a minute and said, "How about the kitchen?"