When a superconductor is put close to a strong magnet, it will lock into the position where it has been put. It will neither fall nor rise. It will not slide off to the side. It will remain where it is relative to the magnetic field.
If the magnet is laid out like a rail in one direction, the superconductor will move freely in the direction of the rail while resisting any other motion.
The simple explanation for this is that the current induced into a superconductor by a magnetic field will produce an equal and opposite magnetic field that resists any change in position relative to the magnet.
This explanation requires no quantum physics. Standard electromagnetic theory is all that’s needed. Move forward to 3:15 in the simple explanation, and the whole thing is explained in a few sentences.
Inducing magnetism into a ferromagnetic rod
The more elaborate explanation, invokes something called quantum levitation. Magnetic field lines are trapped. Quantum flux tubes are pinned in defects, locking the superconductor in space. Move forward to 2:00 in the explanation for the illustration.
The problem with the quantum explanation is that it invokes quantum tubes and field lines, both of which are entirely mathematical concepts.
The simple explanation mentions field lines too, but we can easily model these as high and low pressures in the aether.