Heat energy exchange and the relationship between the temperature of a gas and its volume.
Compression reduces the volume of a gas and thereby increases its temperature. The hot gas is passed through a radiator where heat is transferred through conduction and convection to the external (outside the insulated cavity of the refrigerator cabinet) surrounding air and becomes cooler in its compressed state.
The cooled compressed gas (now at nearly room temperature) is then relieved of its pressure and thereby undergoes further cooling. The gas, now in its coolest state, is passed through another heat exchanger within the food compartment of the refrigerator where it absorbs the heat within and carries it out of the compartment and back to the compressor where the cycle is repeated.