AC synchronous motors are AC motors whose rotation rate is equal to the frequency of the applied voltage frequency. AC synchronous motors have multi phase electromagnets in their stators which create a magnetic field. Due to the magnetic field created in the stator, the rotor which has permanent magnets or electromagnets starts rotating in the same rate and consequently another synchronous rotating magnetic field is created inside the motor.
To rotate a motor, a rotary magnetic field has to be created. In AC synchronous motors, the magnetic field synchronously rotates with the applied voltage. The reason for calling these motors synchronous motors is because their rotation rate is equal to the frequency of the applied voltage. AC asynchronous motors rotate slower than applied voltage frequency. Synchronous rotation of an AC synchronous motor depends on the number of pole pairs and frequency.
Synchronous rotation rate is not dependant on the load of the motor. The rotor rotates at the same rate of the rotating magnetic field rate.