I did not know that yesterday!

Despite its name, dry cleaning is not completely dry. As a matter of
fact, according to several sources I found, dry cleaning uses liquid chemicals to remove stains and clean clothes. I first visited How Stuff Works, which explained that in the early days of dry cleaning, the solvent used was often kerosene or gasoline. That has changed, and the industry now uses perchloroethylene (also
known as "perc") almost universally. Clothes are washed in this solvent, and then the solvent is recaptured so it can be reused.

The EPA's web site also offers some facts on the dry-cleaning process and how it typically works:

Spots are usually treated by hand and then clothes are placed in large machines.
Liquid solvents, detergents, and sometimes a small amount of water are added to the machines, which agitate the clothes in a manner similar to regular washing machines.
Once clean, the clothes are dried, pressed, and shaped. The solvent is separated from waste residues, such as detergents, dye, dirt, and oil, and cleaned so it can be reused.

Finally, the filters used to clean the solvent and the solvent residues are managed and disposed of as hazardous waste. They are usually sent to special facilities for recycling or incineration.

Many people oppose the use of perc, a toxic chemical with both health and environmental concerns. Both of the aforementioned sites provide information on the hazards of this chemical. So read up before your next trip to the cleaners.