How is stable levitation possible?

I tried to add this as a comment, but it is too long so I am making this an answer instead. This is not my text, but the text of one of the commentators on the 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 :)

There is an easy trick behind this. Look closely at the video, the superconducting disc is levitating above several small magnets. The magnets are placed in a checkerboard configuration:

+ - + - + -

- + - + - +

+ - + - + -

Now draw the magnetic flux lines for this configuration. It will basically look like a lot of rings going in and out of the magnets. With this configuration you can already levitate a small piece of graphite because of the high diamagnetism. With a type 2 superconductor another phenomenon locks the disc above the magnet: As FrankH already mentioned you the flux lines will penetrate the superconducting disc if you force it in this position. Due to small impurities you will have areas in the material that are not superconducting and the flux lines will stick to those areas. This is the energetically most favorable state.

If you try to move the disc these flux lines have to move from the impurity site through the material and create small non-superconducting areas which is energetically unfavorable (you lose the condensation energy in those areas).

The locking of the flux lines can be much stronger than gravity and is already used to levitate trains (Maglev).