When you compress a gas - say, a volume the size size of a beachball and it squeeze it into a volume the size of a golf ball - also condenses all of the heat that was in the gas in the beachball into the golf ball size. This makes the compressed golf ball volume hotter than when it was the size of a beachball. If you cool the golf ball down to room temp using a fan, then release that gas back into the beachball, the beachball will be much colder than room temp.

That’s how refrigeration works, in principle. In practice, the gas is a special gas that works more efficiently than air, and the process of compression-cooling-decompression runs in a continuous loop (as long as the compressor is running).