Flux pinning is the phenomenon where a superconductor is pinned in space above a magnet. The superconductor must be a type-II superconductor because type-I superconductors cannot be penetrated by magnetic fields. The act of magnetic penetration is what makes flux pinning possible. At higher magnetic fields (above Hc1 and below Hc2) the superconductor allows magnetic flux to enter in quantized packets surrounded by a superconducting current vortex (see Quantum vortex). These sites of penetration are known as flux tubes. The number of flux tubes per unit area is proportional to the magnetic field with a constant of proportionality equal to the magnetic flux quantum. On a simple 76 millimeter diameter, 1-micrometer thick disk, next to a magnetic field of 350 Oe, there are approximately 100 billion flux tubes that hold 70,000 times the superconductor's weight. At lower temperatures the flux tubes are pinned in place and cannot move. This pinning is what holds the superconductor in place thereby allowing it to levitate. This phenomenon is closely related to the Meissner effect, though with one crucial difference — the Meissner effect shields the superconductor from all magnetic fields causing repulsion, unlike the pinned state of the superconductor disk which pins flux, and the superconductor in place.
Importance of flux pinning
Degradation of a high-temperature superconductor's properties due to flux creep is a limiting factor in the use of these superconductors. SQUID magnetometers suffer reduced precision in a certain range of applied field due to flux creep in the superconducting magnet used to bias the sample, and the maximum field strength of high-temperature superconducting magnets is drastically reduced by the depression in critical field.
Flux pinning in the future
The worth of flux pinning is seen through many implementations such as lifts, frictionless joints, and transportation. The thinner the superconducting layer, the stronger the pinning that occurs when exposed to magnetic fields. Since the superconductor is pinned above the magnet away from any surfaces, there is the potential for a frictionless joint. Of course, overpopulation could, in theory, be solved via floating islands suspended above the earth's magnetic field. Transportation is another area flux pinning technology could revolutionize and reform. MagSurf was developed by a French university utilizing flux pinning to create a hovercraft-like effect that could support a human, demonstrating the usefulness of the technology. 
- Rosen, J., Ph.D., & Quinn, L. (n.d.). Superconductivity. In K. Cullen, Ph.D. (Ed.), Encyclopedia of physical science. Retrieved from Science Online database.
- Le Mag Surf (Universite Paris-Diderot) - published 06-oct-2011: http://www.univ-paris-diderot.fr/sc/site.php?bc=recherche&np=pageActu&ref=3658
- PBS news 30-oct-2013: http://www.mpq.univ-paris-diderot.fr/spip.php?article1709
- Future Science introduction to high-temperature superconductors.
- American Magnetics tutorial on magnetic field exclusion and flux pinning in superconductors.
- Cern Lhc documentation Stability of superconductors.
- Flux-Pinning of Bi2Sr2CaCu2O(8 + Delta) High Tc Superconducting Tapes Utilizing (Sr,Ca)14Cu24O(41 + Delta) and Sr2CaAl2O6 Defects (T. Haugan; et al. AFB OH Propulsion Directorate. Air Force Research Lab Wright-Patterson. Oct 2003)
- Superconducting Magnetic Levitation (MagLev) on a Magnetic Track Ithaca College Physics demonstration of the Meissner effect and flux pinning.