The hot dense gas from the compressor is run through the condenser, which is just another radiator in front of the standard engine cooling radiator. Airflow through the condenser fins removes heat from the gas flowing through the tubes in the condenser, which causes the gas to condense into a liquid form; hence the name "condenser" instead of "radiator" (same kind of device, just different names). All "radiators" are heat exchangers; they exchange heat from one place to another. In these cases we’re removing heat from the engine coolant and the compressed gas refrigerant and exchanging that heat to the atmosphere. We give this condensing radiator a special name, mostly because there are two radiators in the A.C. system and we need to keep them straight. Besides, we already have a radiator for the engine, so let's not call all the heat exchangers "radiators".
The condenser is buried in the bodywork at the front of the car; if you remove the grille, it's the radiator you see when you look into the grille opening.
WARNING: Don't disconnect the hoses from the condenser just for the heck of it, even if the system is discharged. The hose fittings tend to seize on the aluminum fittings on the condenser. If this happens, you can ruin both the condenser and the hoses.