This method is often called "dry cleaning" since virtually no water is used.
In this method, dry absorbent compound (containing small amounts of water, detergent, and solvent,) is sprinkled over carpet or worked into the carpet with a machine. This purpose of this cleaner is to attract and absorb soil. Mechanical agitation from a brush works the cleaner through the carpet.
These products usually contain an absorbent carrier, water, detergent, and solvent. The theory is that the liquids dissolve the soil and this soil/detergent/solvent mixture is absorbed into the carrier and is then vacuumed up. They are often used with a detergent pre-spray in heavily soiled areas.
The absorbent cleaner most commonly is organic (CORN COB), but may also be polymers. The compound is supposed to absorb the dislodged soil and is then vacuumed away. Carpet must be thoroughly vacuumed before and after cleaning.
Very thorough vacuuming should be used to ensure that most of the carrier comes out of the carpet. With the extremely fine powder types, indoor air quality can be reduced. If a white powder starts appearing on shoes and cuffs of pants, too much was used and it was not thoroughly vacuumed up.
This cleaning method has the advantage of no drying time for interim maintenance, since little water is used. However, this method tends to leave a residue.