Degenerate Pressure
When atoms are subjected to extremely high temperature and pressure,
the atoms are stripped of their electrons. In other words, they
become ionized. The pressure of the gas inside of a star is due to
the electrons, or the electron pressure. If the density is high, the
particles are forced close together. The law of physics put
constraints on the motion of the electrons. Electrons are only
allowed to exist at certain energy levels, and no two electrons are
allowed to exist at the same level (unless they spin in opposite
directions). Therefore, in a dense gas, all of the lower energy
levels become filled with electrons. This gas is termed
degenerate matter. Electrons in this state exert a degenerate
electron pressure which resists the force of gravity trying to push
them closer together (because if they were pushed closer together, their
energy would change and they would have to exist in an energy level
that is already filled, which they can't do).
The same thing occurs in neutron stars, but in this case the degenerate
pressure is due to neutrons rather than electrons. In neutron stars,
the gravitational pressure is higher, high enough to push protons and
electrons close enough together that they combine into neutrons. The
neutrons are then pushed closer together until gravity is balanced by a
degenerate neutron pressure.