This was a little demo for my 2nd year teaching laboratory (all credit to Stephen Porter, he made the sample and organised the demo). The black disc is made from YBCO (yttrium barium copper oxide). When it's cooled by liquid nitrogen down to 78 K (-195°C), it becomes superconducting. This causes the little magnet to levitate above it due to the Meissner effect.
When a superconductor is in the Meissner state, it stops any magnetic fields from entering it. This means that they effectively become mirrors for any magnetic fields, so the little magnet sees an equal magnetic field being reflected back at it. Since like magnetic poles repel, the magnet is able to levitate above the superconductor.
The critical temperature for YBCO to become superconducting is around 93 K (-180°C), so it can easily be reached using liquid nitrogen, which is common in most labs. This means that even though it's around 200°C below room temperature, YBCO is still classed as a "high temperature" superconductor!