Moving electrons in a magnetic field feel a force perpendicular to their direction of motion. For an electron orbiting around an atom, if this force is in the same direction as the electrostatic attraction of the nuclei, then the radius of the orbit will compress. If the force is opposite the attraction of the nuclei, the orbit will expand. This creates a difference in the magnetic moment from electron orbits going clockwise vs. counterclockwise with respect to the applied magnetic field (without the field, the orbital moments should cancel). This creates a small diamagnetic susceptibility (meaning it aquires a magnetic polarization opposing an applied field) for ALL atoms, not just what we normally consider to be magnetic atoms. Diamagnets feel a repulsive force from areas of higher magnetic field, which is how the levitation effect is created.
This diamagnetic susceptibility is small compared to what you get in typical magnetic materials (which is why it gets ignored if there is any paramagnetic susceptibility). In typical magnetic materials, the change in magnetic moment comes from reorienting the spin moment of electrons themselves, not from changes in their orbital moments. With paramagnetism or ferromagnetism (where the polarization is parallel to the field, not anti-parallel), the material is always attracted to areas of higher magnetic field. Since the force is attractive, it is not possible to create a stable levitation scenario with a paramagnet without active feedback to control the field, since the closer the material gets to the high-field region, the harder it gets attracted, so any perturbations will make the object either stick to the magnet itself or fall away.