Air conditioners have a cold coil called an evaporator inside. On the outside, they have a hot coil, called the condenser, which releases heat. A pump moves a refrigerant between these two coils: When the liquid refrigerant is in the indoor coil, it evaporates (hence the name), cooling the air around it. Then the hot gas is pumped out into the condenser, where it reverts back to a liquid. These are the same basic components of a refrigerator, by the way.
Chlorofluorocarbons (CFCs) were the most common refrigerant until 1995, when production of these ozone-depleting chemicals was stopped. Modern-day devices mostly use halogenated chlorofluorocarbons (HCFCs), but those will be completely phased out by 2030.