I was reading last night and...
The magnetic field lines are entering the Abrikosov vortices - miniature supercurrents (suppercurrent cells) around the non-superconducting impurities in a very thin, type 2 superconductor. Here, the flux lines form a "flux tube". The flux tubes are difficult to displace in any direction in space, so the superconductor is trapped, locked by the magnetic field.
The size of a single vortex is about the coherence length (a kind of correlation length) of the given superconductor. The vortex is bound by the London penetration depth - the size to which the magnetic field can penetrate near the surface of a superconductor. The superconductors tend to remove all field lines from their insides by means of resistance-free supercurrents that flow in the presence of the field.
So, the point is that the superconductor possesses the particular microscale structure built from vortices of supercurrents.
When you attempt to move the superconductor, there is a minute difficulty followed by a stable, fixed position in the magnetic field. This property is periodic in space, probably in relation with the distinctiveness of individual flux tube positions.
[This is from wikipedia, with the imagination filling in for the most part.]