What is the relationship between American history and American literature? For instance, The Great Gatsby?

While great American literature is timeless, there is, indeed, a connection between a work and its historical setting as well as the era in which the author has lived.  After all, literature is the recording of human experience, and that experience derives from the historical incidents as well as the thinking of its era.

For one thing, the preoccupation with certain themes in a short story or novel is very reflective of the thinking and literary movement of the time in which the work is written.  For instance, Hawthorne's works reflect his angst over the "sins of the father," his relatives who participated in the Salem Witchcraft trials and the religious hysteria of Puritanism.  Herman Melville, a dark Romantic, broods extensively upon metaphysical ideas.  Ernest Hemingway, a Modernist of the big wars era, searches for a solution to the guilt and alienation that man feels in his time.  John Steinbeck, a contemporary of Hemingway, also agonizes over the alienation of men in the Depression Era.

Clearly, the historical events and influences of their country as well as the literary movement and thinking of their times are tied inextricably to the creative process of writing literature for American authors. Often, as in the example of F. Scott Fitzgerald's The Great Gatsby, a literary work is a tableau of its times.