The evaporator core transfers heat from the passenger's compartment to the refrigerant as it passes through the core. It's then passed to the accumulator or compressor, and on to the condenser. The system's condenser then releases this heat from the refrigerant to the atmosphere.
Refrigerant has a very low boiling point and enters the evaporator as tiny droplets. These droplets boil and convert from a liquid to a vapor. Evaporators also remove humidity from the cabin air. Condensation forms on the fins as the hot cabin air passes by. It drips into the evaporator case and then drains through the evaporator case drip tube. This is why clear liquid can be seen dripping from the bottom of the vehicle when the air conditioning is running on a hot, humid day.