The movie Avatar got me interested in the subject, but so far I only found sophisticated articles loaded with unfamiliar words. Is there a simple way to explain how magnetic field affects superconducting materials in a way that causes them to float?
Answer
Superconductors float not just because of the Meinssner Effect. They Float because of quantum locking. Very small weak points in a thin superconductor allow magnetic fields to penetrate, locking them in. These are called Flux Tubes.
The Meissner Effect is only if you make a conductor into a superconductor while the magnet (or magnetic field) is near it. Placing a magnet near an existing superconductor is an example of electomagnetic induction producing magnetic levitation.
Most examples of the Meissner Effect and Electromagnetic Induction are done with a floating magnet. Attempting to float a thick superconductor without quantum locking would quickly cause it to fly off due to unstable magnetic fields. Any example of a floating superconductor is done with a thin superconductor exhibiting quantum locking.
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