Hi
Induction stove works on the principle of electromagnetic induction and EDDY currents. Its basically a transformer with your utensil acting as a shorted secondary. The primary coil is embedded just below the heating surface. When a ferromagnetic utensil is kept on the surface, it acts as a shorted secondary which induces heavy eddy currents in the secondary (utensil) which heats up the food. In this case, for the food, the container acts as the heat source (this is the reason why food seldom gets stuck on the container and also the container gets heated up very slowly resulting in very less heat loss and the efficiency is very high (close to 90% or more).
If the material of the utensil has a greater area under the hysteresis, then heating will also be contributed through magnetizing and De-magnetizing effect (apart from eddy currents). The frequency is used such that it has optimum skin depth for typical utensil thickness.
At a circuit level, it is basically a LC tank circuit which is energized via a H-Bridge circuit (typically implemented using IGBTs due to higher operating power).
The best part about induction stove is that it consumes very less power due to the switching nature of circuitry. When you don't place a container on the stove or place a non-ferromagnetic container, the secondary acts as an open circuit and the current sensing circuit in the primary will turn off the device.
The only drawback i see is the material dependence and flat bottom utensil requirement.
I have one at home.
regards
Darkseid