1) An induction stove works on the principle of electromagnetic induction.
2) A metal coil is kept just beneath the cooling surface. It carries alternating current (AC). So that AC produces an alternating magnetic field.
3) When you keep a metal pan with water on it, the varying magnetic field beneath it crosses the bottom surface of the pan and EMF is induced in it.
4) Since pan has a finite resistance, the flow of induced current in it produces heat in it and this heat is conducted to the water.
5) That's why we call this stove as induction stove.