Think of it like this: the refrigerant starts as a low-pressure, low-temperature gas. The compressor takes this gas and squeezes it, significantly increasing its pressure and temperature. This high-pressure, high-temperature gas then moves to the condenser, where the heat is released to the outside environment. After that, the refrigerant is converted back to a low-pressure, low-temperature liquid to start the cycle again.
In short, the compressor is responsible for the circulation and pressure changes of the refrigerant, making the entire air conditioning process possible. Without a functioning compressor, your AC system won't work.