Tom Hanks plays Joe Banks, a man who hates his job, thinks the overhead fluorescent lights are making him sick, and quakes at the presence of his boorish boss Frank Watori (Dan Hedaya). He is attracted to the office secretary DeDe (Meg Ryan) but is afraid to speak to her. Then his life changes when he visits Dr. Ellison (Robert Stack).
Dr. Ellison tells Joe that he has something called a brain cloud that is rapidly spreading throughout his brain. He will feel great, but he'll be dead within five months. Instead of being depressed at this bleak prognosis, Joe suddenly feels free. He quits his job, asks DeDe out, and is contacted by a rich millionaire named Graynamore (Lloyd Bridges).
Graynamore owns an island named Waponi Woo, whose natives need to be placated. The natives require a sacrifice to their island volcano, the Big Woo, so that the island won't sink beneath the Pacific. Graynamore offers unlimited wealth to Tom in exchange for Tom's becoming the object of human sacrifice. Joe has nothing to lose, so he accepts the offer.
As he heads out to the island, Joe meets Graynamore's daughters -- Angelica, a Los Angeles socialite, and Patricia, Angelica's blonde half-sister (both roles played by Ryan). Joe arrives at the island, and as he stands at the lips of the Big Woo he has to decide whether he really wants to leap into the maw of the fiery volcano.