Usually breadcrumbs or cheese sprinkled on the top of a dish, placed under a grill for a few minutes to finish and brown makes it au gratin.
Gratin dauphinois is a classic dish; gratin savoyard, made with sliced potatoes, Beaufort cheese, butter and bouillon is another. Many baked pasta dishes, or baked dishes in a sauce, are often finished au gratin to make them more appealling.
The French upper class is the gratin of society.
Image by pelican