The "volumetrics" approach differs from the grapefruit diet™, the Adkins diet, the Summers diet, Jenny Craig and all the rest. On the Volumetrics diet, your goal is to eat food with water and fiber. Fresh fruit, fresh vegetables, soups, stews, seafood -- things that fill you up quicker than other foods do. By eating "filling" foods, you feel full quicker and, in theory, eat less.
If you divide the number of calories in one serving of food by its weight in grams, items with a density of two can be consumed often. Things more dense (a higher number) should be eaten less often.
There's a fairly extensive list of suggested foods for the volumetric diet.