An air conditioner is basically a refrigerator without the insulated box. It uses the evaporation of a refrigerant, like Freon, to provide cooling. The mechanics of the Freon evaporation cycle are the same in a refrigerator as in an air conditioner. According to the Merriam-Webster Dictionary Online, the term Freon is generically "used for any of various nonflammable fluorocarbons used as refrigerants and as propellants for aerosols."
 

Diagram of a typical air conditioner

This is how the evaporation cycle in an air conditioner works (See How Refrigerators Work for complete details on this cycle):

1. The compressor compresses cool Freon gas, causing it to become hot, high-pressure Freon gas (red in the diagram above).
2. This hot gas runs through a set of coils so it can dissipate its heat, and it condenses into a liquid.
3. The Freon liquid runs through an expansion valve, and in the process it evaporates to become cold, low-pressure Freon gas (light blue in the diagram above).
4. This cold gas runs through a set of coils that allow the gas to absorb heat and cool down the air inside the building.

Mixed in with the Freon is a small amount of a lightweight oil. This oil lubricates the compressor.