Well, you probably know colder air has higher density (or conversely, that hot air expands). Now a jet turbine compressor stage, just like a turbo on your car,

Well, you probably know colder air has higher density (or conversely, that hot air expands). Now a jet turbine compressor stage, just like a turbo on your car, moves a fixed volume of air per second into the combustion chamber. But the actual combustion cares about the mass of air (well, oxygen). So a higher density/lower temperature gives you more power with the same turbo. This is why cars have intercoolers.