Most AC motors are three-phase or single-phase. Inside a three-phase motor there is a stator made of three pairs of coils and a rotor that houses a permanent magnet or a set of windings. The stator coils are supplied by a three-phase power line, featuring a phase angle shift of 120°. Each coil puts out an alternating magnetic field depending on the direction of the current flow. Since the coils work together they generate a rotating magnetic field, which lets the motor spin.
In a synchronous motor a permanent magnet spins at the synchronous speed of the rotating magnetic field, which depends on the supply frequency.
In an asynchronous motor there is a set of rotor windings shorted or closed through resistors.
The rotor will never reach the synchronous speed, otherwise the e.m.f. induced in the rotor windings would be null.
A single-phase motor works due to the same principle. The stator houses two sets of coils. One of them is connected in series with a capacitor, so there are two currents featuring a phase shift of about 90°. In other words it is a sort of two-phase power line.
The coils connected with the capacitor often switch off once the motor spins in the correct direction, so they are called start coils.