I learned this game from a fellow teacher in the Intensive English Learning Program at LaGuardia Community College, CUNY, who played it as a child.
It's a pairs game (or chain game), where each player picks up from the previous player's contribution.
The joker starts the game, usually with the standard opening, "Unfortunately, I fell out of an airplane."
The next player continues the story, but switches the direction, "Fortunately, I had a parachute."
The joker (or a third player, if it is a chain), continues, "Unfortunately, the parachute had a hole in it."