This phenonemom has also been called Quantum Locking. The term Quantum comes from the fact that superconductivity is a quantum phenomenon and the Locking comes from the fact that magnetic fields are confined or locked into narrow tubes going through the superconductor. In terms of applications - this is basically a form of magnetic levitation using superconductivity so there may be practical applications but there will also be limitations due to the cooling required for superconductivity (at least today) and there are also limits to the weight that can be supported.
See this very similar question about stable levitation and my answer. A slightly edited copy of the answer is reproduced here:
The text below is not my text, but it is the text of one of the commentators on the original video:
"Superconductors are of two types, which are defined by their Meissner effect. One type repels magnetic fields, which will levitate the superconducting object. A type I superconductor becomes a perfect diamagnetic material, which exhibits a magnetization in the opposite direction of an applied magnetic field. The Meissner effect creates a complete diamagnetic material so that no magnetic field lines are present in that material. I doubt this will suspend the object against gravity by putting it on bottom, for the magnetic fields in opposition will impose a force on the superconductor in the same direction as gravity.
There is what might be called an anti-Meissner effect where the superconducting material collimates magnetic flux lines into narrow tubes or vortex fluxes. If the magnetic field at large is not perfectly uniform it takes work to move the object through the magnetic field and so energetically it is favorable to remain in a region with $B_{in}$ and $B_{out}$ remains the same. This is the Landau-Ginsburg effect and is found in type II superconductors. I think that this is a case of a type II superconductor."
This sounds right to me and explains what is meant by quantum locking since superconductivity is a macroscopic quantum phenomenon that is effectively locking the magnetic flux into specific tubes in the superconductor. The force that opposes gravity is, of course, magnetic so we are not talking about any kind of new force of nature.
When he uses his hand to move the superconductor, he is using enough force to make the magnetic flux tubes be rearranged but apparently the force of gravity is weak enough such that it cannot rearrange the flux tubes by itself. So I predict that if you added enough weight to the puck, it would fall.