A magnet will float above a cold metal

A superconductor expels magnetic fields. A magnet placed over it levitates, held by the currents the field itself induces.

Meissner and Ochsenfeld found in 1933 that a superconductor does not merely keep a field from getting in. It pushes an existing field out as it cools through the transition. Surface currents arrange themselves to cancel the field inside. A magnet above that surface sits in a well.

Type-II superconductors, the ones in the classroom demo, pin the field in tubes and will hang below a magnet as well as float above it. The toy is a macroscopic quantum effect you can balance a coin on. The resistance underneath is exactly zero, which is the other half of the weirdness.