A degenerate gas is a gas that has been compressed to the point where the wave functions of the atom's electrons are touching. Once you reach this point the ideal gas law fails. You can heat a degenerate gas all day long and never get an increase in pressure. This is what causes the helium flash in a star.

If you have no idea what I just said think about it like this. Think of a gas atom as a ball bearing inside a ping pong ball. The ball bearing is the nucleus and the ping pong ball is the wave function for the electron. As the ping pong ball vibrates around it will hit other ping pong balls. The frequency of these collisions is pressure. If all the ping pong balls are touching then they have the max pressure they can have because they have infinite collisions. Now if you heat up the gas the ping pong balls get hotter but no pressure is added because you can't squeeze them tighter together. This cause more heat to be created in an exponential form until the degeneracy is broken and the ping pong balls separate.

I was asked to explain why this is not a solid. In a solid the wave pattern, i.e. the ping pong balls are not just pressing up against one another but they have broken and now overlap each other. This is a very simple explanation but a full explanation belongs in another node.