Inverter supplies variable frequency alternating current to AC motor of compressor to control its speed. In case of DC motor, variable voltage is supplied to control its speed.
These days DC motor is commonly used in Inverter air conditioner's compressor as it's more power efficient. (inverter is not technically utilized but inverter name for energy saving air conditioners will prevail)
Non-inverter traditional air conditioners' compressor run at fix speed and have poor temperature control mechanism.