You must be aware of rotating magnetic fiel if not please refer my answer for this ques: How synchronous motor is independent of voltage change explain briefly? Now you know what is rotating magnetic fiel you think how fast it is rotating? This stator may be single or three phase.
Now, if we supply ac to stator,a magnetic field will produce in rotor,and rotor will rotate in synchronous speed with stator field. It does not require nay external mean to rotate.
However, in this case, the rotor has its own field produced by .
Synchronous motors are inherently not self starting.
They require some external means to bring their speed close to synchronous speed to before they are synchronized. The speed of operation of is in synchronism with the supply frequency and hence for constant supply frequency they behave as constant speed motor . This video is about the reason that synchronous motor is not self - starting ? Working of synchronous motor is elaborately explained in this video animation.