Electron degeneracy pressure is an exact materialization of the more general phenomenon of quantum degeneracy pressure. The Pauli Exclusion Principle disallows two identical half-integer spin particles, including electrons and all other fermions, from concurrently occupying the same quantum state. The result is an emergent pressure against compression of matter into smaller volumes of space.
Electron degeneracy pressure occurs from the same underlying mechanism that defines the electron orbital structure of elemental matter. For bulk matter with no net electric charge, the hold between electrons and nuclei exceeds, at any degree, the mutual repulsion of electrons and the mutual repulsion of nuclei.
So, without absent electron degeneracy pressure, the matter would collapse into a single nucleus. In 1967, theoretical physicist and mathematician Freeman Dyson showed that solid matter is stabilized by quantum degeneracy pressure rather than electrostatic repulsion. Because of this, electron degeneracy creates a barrier to the gravitational collapse of dying stars and is responsible for the formation of white dwarfs