Atomic Origin of Diamagnetism
The motion of orbiting electrons in atoms is changed by an applied field, producing an opposite magnetic moment.
When a field is applied to many atoms, the opposite dipole moments m provide fields that partly cancel the magnetic fields that induced them.
This weakens the magnetic field inside diamagnetic materials, “forcing out” field lines.
Because all atoms have orbiting electrons, you might expect all materials to by diamagnetic, and that’s true so far as it goes. If electrons and nuclei didn’t themselves act like little spinning magnets, all materials would indeed be diamagnetic.
Diamagnetism tends to be a very weak effect in almost all materials, but there are some materials, called superconductors, where it can be a huge effect indeed, because it is the free conduction electrons that produce the diamagnetism in that case.
In the illustration at bottom left, notice how the density of field lines is smaller inside the dielectric material than outside it because the field lines have been forced out by the diamagnetic effect. This reduced density of lines happens because the magnetic forces on the orbiting electrons create currents in the opposite direction from the field.