To simplify a bit more, here are the basics of refrigerant system operation...
Think of the system as not cooling so much, as removing the heat from the intake air charge. The air returned is in actuality having heat removed from it, rather than actually 'cooling' it per se. The refrigerant is in a constant loop of circulation, changing between liquid and gas forms to transfer this heat elsewhere from where it is not desired. You have four basic components in the system...
1) The compressor (the 'heart' of the system, as it were)
2) The condenser core/coil
3) The receiver / drier / orifice tube assembly
4) The evaporator core/coil (where the magic happens)
As the compressor runs, it sucks in low-pressure, gaseous refrigerant, compressing it and creating the high-pressure / liquid side of the system. The old scientific principle of heat expanding and cold contracting is in play here. When the refrigerant leaves the compressor, it takes a liquid form, entering the condenser.
Air blown across the condenser coil cools the liquid as it travels through it. It remains liquid and high-pressure as it enters the receiver/dryer/orifice tube assembly.
The orifice tube filters and meters the flow of refrigerant into the evaporator core, where it expands to return to a lower-pressure, gaseous form, getting super-cold in the process. This is where the system 'sweats', or condensates, forming condensation on the outside of the receiver/dryer and the nearby lines. This is due to the extreme drop in temperature, especially against the higher underhood temperatures around these components.
The air inside the vehicle is drawn across the evaporator, where the refrigerant, now expanded and super-cold, absorbs any heat from the air drawn across the evaporator.
The refrigerant, still in low-pressure, gaseous form, enters the compressor to complete the cycle, where it is compressed, returning to a high-pressure / liquid form before carrying the absorbed heat away to be exhausted through the condenser coil.
And that, boys and girls, is how refrigerant systems work. Some systems have an expansion valve rather than an orifice tube, but the principle of operation is the same, whether it is a car, van, SUV, window-shaker, freezer, or refrigerator. Heat pumps operate pretty much the same way, except they have additional components to essentially reverse refrigerant flow.
Here is a diagram to help to understand the process... You can clearly see how cooling the condenser coil properly is vital to proper and continuous system operation.