The musical is based around the some of the subcultures of 1950s high school America, including the "tough guy" working-class greasers from which the musical takes its name. In the film, Travolta played Danny Zucko, who is trying to win the affections of Australian exchange student Sandy (Olivia Newton-John).
The movie version sugar-coated the class aspects of the original, and subsequent stage productions have played down that aspect of the story even further and emphasised the nostalgia aspects. A sequel, "Grease 2" (1982) moved the timeline forward to the early 1960s, and reversed the gender plotline (a male newcomer from England trying to woo the leader of the Pink Ladies), using motorcycles instead of cars.
A more dramatic, harder-edged portrayal of some of the same subcultures (though slightly later) can be found in S.E. Hinton's novel The Outsiders.