An air conditioner works as a heat exchanger. It takes in warm air in your room and passes it over a set of cooling coil and then blows it back to the room as cold air. The cooling cycle of your air conditioner involves two basic processes: condensation and evaporation (you must have learned about them in school).
There are 4 important components in your AC that control the cooling cycle:
Freon- Cooling agent
Compression and condensation cycle
The coolant (mixed with lubricating oil*) enters the compressor as a cold low pressure gas where it is compressed. This compression increases the temperature and pressure of the coolant which converts it into a hot high pressure gas. This hot high pressure gas passes through a series of thin coil called condenser coil where it gets converted into a high pressure liquid. Whenever gas is converted into liquid heat is released. So the heat released during condensation of coolant is dissipated outside with the help of a condenser fan (located next to condenser coils).
Expansion and evaporation cycle
This hot high pressure liquid then passes through an other set of thin coils called evaporator coils, where it gets evaporated into a low pressure gas. As the liquid changes to gas and evaporates, it extracts heat from the surrounding warm air of your room. So the air coming in contact with these coils get cooled and is blown back to the room with the help of an evaporator fan.
By the time the working fluid leaves the evaporator, it is a cool, low pressure gas. It then returns to the compressor to begin its trip all over again.