About Magnetic Levitation
Magnetic levitation can be achieved either one of two ways. The naive approach (and I say that from experience) is to take two magnets and attempt to balance them with like poles repelling each other. As anyone who has tried this knows, the magnets never balance quite completely and the attempt is rather futile. This can be slightly improved upon by using a gyroscope to balance to the hovering magnet, as is done in the popular Levitron--though this too is rather finicky and frustrating at moments. The bottom line is such contraptions are inherently unstable, and the unstable equilibrium of such approaches is summarized mathematically by Earnshaw's Theorem.
The second and better way to go is to induce an electromagnet that will repel the physical magnet instead. This is achieved through magnetic induction: as a magnet is lowered towards a conductor eddy currents are induced according to Faraday's and Lenz's Law to repel the magnet being lowered. Why might this way be more stable you ask? The induced electromagnet effectively allows for more "degrees of freedom" as the eddies are induced in all directions, in just the right way to repel the magnet. In short, Nature does the work and she always does it perfectly.
Magnetic levitation is not confined to superconductors and can be achieved, for brief moments of time, even with highly cooled, non-superconducting materials such as copper. The eddy currents induced under normal circumstances however die out quickly as a result of the electrical resistance present within all conductors (like aluminum, copper, gold, etc). However in a superconductor--a material in which there is zero (yes, exactly zero) electrical resistance--these currents persist and continue to levitate the magnet perpetually. These persistent currents allow the electromagnet to push on the physical magnet indefinitely, and thus are the critical advantage to magnetic levitation using superconductors.
