Who can explain this?

Magic!

Naw! It's smoke and mirrors. Didn't you see the smoke?

It is just a demonstration of the Meisner effect for a superconducting material. In fact, if the pictured apparatus had the superconducting material (the black cube) attached to the dish that holds the liquid nitrogen, the entire thing could be tipped on its side and the rotating magnet would still hover directly over the cube, it would not slide out of the magnetic field. That's way more impressive than just floating.

Dennis

The black block is a high-temperature superconducting material. The silver disk is a strong magnet. When the superconductor is cooled with liquid nitrogen and becomes superconduction, any movement of the magnet generates an opposing eddy current in the superconductor. By Lenz's law, this eddy current produces an opposing magnetic field that opposes any movement of the magnet. Since there is no resistive loss in the superconductor, the magnet just stays where it is left.

Thank you Bob.