A white dwarf is a star formed when a red giant runs out of helium fuel after losing most of its mass into space. This leaves only the core, which is not producing any heat via nuclear fusion. As a result there is nothing to stop gravity collapsing the core down to a very small size (~10km). At this point the electrons in the core are so closely packed that quantum effects provide a counter force and the core stabilises.
The resulting white dwarf is extremely hot and dense, although not as dense as neutron stars or black holes. Because they contain only residual heat from the stellar lifetime, white dwarfs eventually cool to become black dwarfs.
In 2364, the USS Tsiolkovsky was observing the formation of a white dwarf when its crew succumbed to polywater intoxication. The USS Enterprise-D, sent to investigate, was subsequently threatened by a stellar core fragment thrown off by the collapse of the red giant. (TNG: "The Naked Now")
White dwarfs are the only natural source of vertion particles. In 2370, a network emergent circuit nodes aboard the Enterprise-D collected vertions from the white dwarf Tambor Beta-6 to sustain their growth, but the supply from a single star proved insufficient. (TNG: "Emergence")