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A foam is a substance formed by trapping pockets of gas in a liquid or solid. A bath sponge and the head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin films of liquid or solid separating the regions of gas. Solid foams can be closed-cell or open-cell.
Soaps contain chemicals called foaming agents. Common foaming agents used in consumer products are the chemicals ammonium lauryl sulfate and -- even more common -- sodium dodecyl sulfate (sometimes referred to as sodium laureth sulfate). Beyond acting as foaming agents, these ingredients also function as surfactants.