It is a gas based "heat pump", in principle the same type of system as a refrigerator or freezer.
The system is partly filled with a liquefiable gas - freon or now sometimes propane.
There are two heat exchangers (radiators, in principle) - the evaporator and the condenser.
A compressor collects gas from the evaporator and pumps it in to the condenser. At that point it is hot - the heat energy in it has been packed ion to a small space.
The condenser is the outside part; it has air blowing over it to cool it.
With a combination of the pressure and cooling, the gas becomes liquid.
It then passes through a control valve or restrictor tube in to the evaporator (the indoor / cooling part).
As the pressure there is kept low by the compressor continuously drawing gas out, the liquid boils, expands and gets very cold - it needs to absorb heat in the process of boiling, so the evaporator gets cold, cooling the air being blown through it!
The whole process runs continuously, until the system or room thermostats cut off the compressor.
The "split" system just has extended pipes between two parts, typically the indoor evaporator section and the rest of the unit.