Object B, a small rare earth magnet is what is being levitated between objects A and C.  Object A is a large magnet which provides most of the lift for magnet B.  Object C is a diamagnetic material (pyrolytic graphite is one of the best materials for this, but bismuth could also work) which provides a very small repulsive force towards object B.  This small force is not enough to even come close to lifting object B, but it is enough to provide the extra force needed to stabilize object B.  Any small variation in the magnetic field generated by object B is compensated for, and a proportional opposing force is generated by object C.  Note that when I mention a "variation in magnetic field generated by object B" this is with respect to object C.  A slight movement by object B would cause a variation of magnetic field by object B towards C.  Also external effects, such as a large metal object being moved, or even a car passing in front of your house will create a variation in the local magnetic field profile which object C also compensates for!  Object C is actually a feedback system that operates on the atomic level.  This makes it very fast, and operate at a very high resolution!  Just imagine object C as a matrix of millions of tiny electromagnets, each controlled by it's own sensor. Each of these little feedback systems compensate for any variation in magnetic field, providing a proportional, but weak, opposing force toward any ferromagnetic object.



Basic definitions:

Diamagnetic material - All materials are diamagnetic, however some will exhibit diamagnetic properties more than others.  Without getting into the physics, diamagnetic materials essentially repel magnets.  It doesn't matter what the orientation of the magnet, a diamagnetic material will adjust on an atomic level to repel the magnet that imposes its field on the diamagnetic material.  At room temperature this effect is very small, and is not nearly enough to levitate an object.

Ferromagnetic material - A material that contains Iron, hence the "Ferro" prefix.  Materials with Iron can become magnetized, at which point they can become permanent magnets.