pandiani, there are lots of different kinds of single phase AC motors, each with a different scheme for getting the motor started.
In the most basic form, you need to create a second AC phase that is offset in time with the primary AC power phase. Once you have created this second phase, you use it to create a spinning field in the stator which drags the rotor around just like in a three phase motor.
Many different schemes have been used to create this second AC phase, some of purely inductive, some using capacitors and inductors, and some using simple magnetic methods as in shaded pole motors.
Most of these develop rather poor levels of torque at start so that becomes a key application issue when selecting the right design of single phase motor.