motor is an alternating current motor
that uses the principles of electromagnetic induction
In a traditional permanent magnet or universal motor, the rotor (the part that rotates) has windings on it that are fed current through a commutator. This produces a magnetic field that interacts with a second field produced by field coils that surround the armature. The good old principles of like-poles-repel/opposite-poles-attract go into effect, and the armature rotates. When the armature has almost rotated such that the magnetic fields align, the commutator reverses the polarity, causing the armature to continue to rotate in the same direction.
Induction motors change all this. The only coils in an induction motor are the field coils. In most motors, these coils are configured such that a rotating magnetic field is produced within. The rotor sits inside this field.
Now, the laws of physics dictate that a changing magnetic field will induce an electric current in a conductor. The rotor has loops of metal within. The changing magnetic field produced by the field coils induces an electric current in these loops. The loops, in turn, produce a magnetic field which interacts with the original field from the field coils. This interaction produces torque which causes the rotor to turn. The rotor will eventually reach near syncrony with the rotating magnetic field. The speed difference between the field and the rotor is known as slip. The field may be rotating at 1800RPM, whereas the rotor might spin at 1750RPM.
Of course, this node is a gross simplification of how induction motors really work. There are so many different types of induction motors, you can write a few books about all of them. However, all induction motors are based on this principle.