Quantum mechanics restricts the number of electrons that can have low energy. Basically, each electron must occupy its own energy state. When electrons are packed together, as they are in a white dwarf, the number of available low energy states is too small and many electrons are forced into high energy states. When this happens the electrons are said to be degenerate. These high energy electrons make a significant contribution to the pressure. Because the pressure arises from this quantum mechanical effect, it is insensitive to temperature, i.e., the pressure doesn't go down as the star cools. This pressure is known as electron degeneracy pressure and it is the force that supports white dwarf stars against their own gravity.