Usually takes the form "Of course I know [famous person]. We grew up/went to school/served in the military/shared a cell in a Turkish prison together. I can certainly get tickets/backstage passes/an interview/other difficult or impossible favor for you, no problem."
Of course, the person making the claim has no such connection to the celebrity in question, and sometimes may not even have a clue of who the celebrity is. The promise is made either in an attempt to look more important than he really is, or out of misplaced sympathy for a friend, a child, or some other "unfortunate" who has failed at the task. The resulting mad scramble to make good on the foolish promise drives at least a subplot (if not the main plot) for an entire episode.