The original game consisted of a single premise: Jumpman, who was a carpenter, needed to rescue his girlfriend, Pauline, from his "crazed" pet gorilla, who'd kidnapped her. The player would have to run, jump, and climb a series of obstacles in an attempt to save her. According to The New Yorker, Miyamoto based the creation of Jumpman on Popeye.
Sources: The New Yorker, Nintendo