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I'll take this one.
Refrigerators and A/C systems work essentially the same way. Refrigerants are weird fluids that are a gas at room temperature and atmospheric pressure but change into a liquid when compressed - 70 PSI (or so) at room temperature.
The fundamental function of the refrigerant is the change from a liquid to a gas. A liquid contains much more heat energy than a gas, and changing a liquid into a gas requires a lot of heat energy.
What happens is your refrigerator pump (or A/C pump) compresses refrigerant into a liquid, pumps it through the condenser (back of the fridge or in front of your radiator) to get this liquid fairly close to ambient temperature. It then goes through a tiny orifice at the entry to the evaporator. What this orifice does is reduce the pressure to below a point that the refrigerant can remain a liquid. The refrigerant then becomes very very cold because it has changed from a liquid to a gas. Changing it into a gas requires a lot of heat energy, which is absorbed from its surroundings. We see it as being very very cold.
Ever open a propane bottle and see how stinking cold the liquid coming out is? Same exact thing.
Your heater fan blows air through the super cold evaporator to cool your cabin. The refrigerant then goes back to compressor where it is compressed back into the condensor. However, it now contains much more heat energy (absorbed in the evaporator) so now that it is compressed back into a liquid, it enters the condensor very hot (too hot to touch) where it is cooled back down. And on to the evaporator again. ETC.
It's all about heat transfer - from the cabin airflow through the evaporator INTO the refrigerant and OUT OF the refrigerant into the airflow through condensor.
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