When you connect a source of three phase power to a three phase motor (of either type), it creates a magnetic field in the stator (the stationary part). This field is felt within the rotor (the moving part). The field will rotate around the stator at a speed determined by the frequency of the source (generally, this is 60 hertz in the US). When I say that the field ?rotates,? I mean that there will be a Magnetic North Pole at the top of the machine at one moment, that a moment later that Magnetic North Pole can be observed at the side of the machine, and a moment later it is at the bottom of the machine, and around the circle it goes.
The term ?synchronous? refers to the fact that the rotational speed of the motor is in exact synchronization with the rotating speed of the magnetic field. If the field rotates at a rate of 20 rotations per second (1200 revolutions per minute), then by golly the rotor will rotate at that exact same 1200 revolutions per minute. It can rotate at no other speed. That is due to the way it is constructed.
The rotor of an ?induction? motor will also rotate in response to the magnetic field that is rotating around it. But it cannot rotate at the same speed. Here again, due to the way it is constructed, it will rotate at a slightly slower speed than the speed of the field. The more load you put on the motor, the slower it will run.
This of course brings up the questions, (1) What is the difference in the way the two are constructed, that causes them to behave in the manner described above, and (2) What are the advantages of one over the other? Those will have to wait for another day.