In general, "degeneracy" means "reverting to an earlier, simpler, state"
In mathematics, a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. See mathematical degeneracy.
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Degenerate matter is matter which has sufficiently high density that the dominant contribution to its pressure arises from the Pauli exclusion principle.
In metals it is useful to treat the conduction electrons alone as a degenerate, free electron gas while the majority of the electrons are regarded as occupying bound quantum states.
In degenerate gases the kinetic energies of electrons are quite high and the rate of collision between electrons and other particles is quite low, therefore degenerate electrons can travel great distances at velocities that approach the speed of light.
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