Jeff the Zookeeper isn’t too good at his job (but then, when was a person with a backwards baseball cap ever good at anything (Lleyton Hewitt notwithstanding)). Hordes of monkeys have escaped from the zoo, and he must return them, alive.
He does this by tempting them with bananas, of which he has a finite supply, before hitting them with a baseball bat to stun them (logically, tranquillizer darts would make more sense, but this way the game involves getting close to the monkeys, making things tougher), before boxing them up (again, the number of boxes is limited) to return safely to the zoo.
The levels on which this must be done consist of a number of platforms, ladders, ledges and the like, and are played against a time limit. Falls stun Jeff, potentially allowing the monkeys time to escape, or drop banana skins to disrupt him.