The term refers to a water bath, either on the stove-top or in the oven. The purpose is to slow the conduction of heat with water, therefore slowing the cooking process. It is used for delicate foods that are ruined by excess heat, such as egg custards, mousses, or chocolate.
A stove top bain-marie is often called a double boiler. The method does not require a special pot, but can be created by setting a heat-proof bowl on top of a simmering pot of water. There should be at least an inch of space between the water and the bottom of the bowl. (If the bowl is touching the water the heat is more direct than if there is a buffer layer of steam.) This method is used for things like melting chocolate, whisking hollandaise, foams for sponge cakes and meringues.
An oven bain-marie is created by placing the pan of food inside a larger pan of water. The method sometimes also requires the entire thing be covered. The water should be at a level at most 2/3 up the side of the pan holding the food. This creates a slow conduction of heat and even cooking. Care must be taken to avoid accidently adding water into the smaller dish inside. This is best done by adding the water to the large pan in the oven, thereby avoiding carrying a sloshy pan of water across the kitchen. This method is used for recipes like egg custards, cheese cakes, foam cakes, and some forcemeat (pâtés, terrines, etc.).