Why does magnesium have a large increase between its second and third ionization energies?

The electron configuration of Mg : 1s² 2s² 2p⁶ 3s²
or simply, Mg : 2, 8, 2

In successive ionizations, the first two electrons are removed from M shell (the 3rd shell), while the third electron is removed from the L shell (the 2nd shell). Much more energy is required to remove an electron from the inner shell (L shell) than the outer shell (M shell), because the electron in the inner shell is closer to the nucleus resulting in a greater nuclear attraction.

Therefore, there is a large increase between the second and third ionization energies.