What you're watching below is an example of diamagnetic levitation. The little bench that the coil is sitting on top of is solid aluminum. The coil is about three inches in diameter and contains a few hundred turns of magnet wire. A variac is used to drive the coil with AC current.
When the coil is energized, the alternating current creates an alternating magnetic flux. This flux sets up a counter-emf, (electromotive force) in the space occupied by the aluminum plate. This counter-emf creates a current in the aluminum plate that in turn creates a magnetic field opposing the one created by the coil. The two magnetic fields repel and the coil is levitated. Check out the videos and then check out the newspaper article from the '60s describing the levitational stove.
NEW YORK HERALD-TRIBUNE: Monday, November 21, 1951, pp. 1 & 6
PAN FLOATS IN AIR
In it seven coils of wire on laminated iron cores are contained inside a plywood cabinet of blond mahogany. The magnetic field from these coils induces 'eddy currents' in an aluminium cooking pan nineteen inches in diameter, which interact and lift the pan into space like a miniature 'flying saucer.'
The cooking pan floats about two inches in tha air above the stove in a stabalized condition; 'eddy currents' generate the heat that warms it while the stove top remains cold. The aluminium pan will hold additional pots and it can be used as a griddle. It is, of course, a variation of several other more familiar magnetic repulsion gadgets including the 'mysterious floating metal ball' of science hall exhibits.