What is the cause of greater stability of exactly half-filled and completely filled configurations?

The greater stability of these configurations is due to following two reasons:
(i) Symmetry. The half-filled and completely filled configurations are more symmetrical and symmetry leads to greater stability.
(ii) Exchange energy. In an atom, the electrons present in various orbitals of the same sub-shell tend to exchange their positions. Such an exchange of electrons results in the release of energy called exchange energy. Greater the exchange energy, more is the stability associated with the orbitals. Now half filled and completely filled sub-shell configurations allow the maximum exchange of electron to take place. Therefore, such configurations have maximum stability.