The thing with that is that it's completely wrong. This has never been done in any high school worth the name. No one would let a vat of liquid nitrogen loose near a group of teenagers, it's a recipe for disaster.
Also, this uses fundamentally different principles than magnetic repulsion, which is what you are referring to. Magnetic repulsion relies on the property of magnets that two magnets of the same polarity will repel each other with a certain amount of force. If one of the magnets weighs less than the other, they will repel each other and the one higher up will float in the air.
This experiment uses a property of superconductors that has absolutely nothing to do with magnetic repulsion. Without a charge running through them, superconductors aren't even magnetic. In layman's terms, superconductors don't like to move through magnetic fields. If you try to push one through a magnetic field, they push back to try and not move. It's really complicated, but the gist of it is that moving around a magnet makes it try to move in the opposite direction.
If the magnetic field is strong enough and/or the push is weak enough, then the superconductor is able to create enough counter force to stop its motion. That's how it is suspended in the air. Gravity is not able to exert enough force to override the counter force.
It moves around circular magnets because of the shape of magnetic fields. The layman's version of that is that because the magnet is a ring, it's moving along the magnetic field instead of through it.