A synchronous electric motor is an AC motor in which, at steady state, the rotation of the shaft is synchronized with the frequency of the supply current; the rotation period is exactly equal to an integral number of AC cycles.
When three-phase electric conductors are placed in certain geometrical positions,an electrical field is generated. The rotating magnetic field rotates at a certain speed known as the synchronous speed. Wath the video from learnchannel for more info:
This motor runs at a constant speed from no load to full load in synchronism with line frequency.Synchronous motors contain multiphase AC electromagnets on the stator of the motor that create a magnetic field which rotates in time with the oscillations of the line current.
The rotor with permanent magnets or electromagnets turns in step with the stator field at the same rate and as a result, provides the second synchronized rotating magnet field of any AC motor. A synchronous motor is termed doubly fed if it is supplied with independently excited multiphase AC electromagnets on both the rotor and stator./wikipedia