A short explanation of how this works:
An object does not need to be superconducting to levitate. Normal things, even humans, can do it as well, if placed in a strong magnetic field. Although the majority of ordinary materials, such as wood or plastic, seem to be non-magnetic, they, too, expel a very small portion (0.00001) of an applied magnetic field, i.e. exhibit very weak diamagnetism. The molecular magnetism is very weak (millions times weaker than ferromagnetism) and usually remains unnoticed in everyday life, thereby producing the wrong impression that materials around us are mainly nonmagnetic. But they are all magnetic. It is just that magnetic fields required to levitate all these “nonmagnetic” materials have to be approximately 100 times larger than for the case of, say, superconductors. This experiment was conducted at the Nijmegen High Field Magnet Laboratory.
(Via food for design)