White dwarfs are the final stage of low-mass stellar evolution.
Low-mass stars, those of roughly 1 to 4 solar masses, undergo a series of evolutionary steps. The evolutionary step right before the star becomes a white dwarf is the ejection of its unfused Hydrogen envelope which then becomes a planetary nebula, which removes ~ 60% of the star’s matter. The remaining core, made up of Carbon and Oxygen then cools and condenses, as it was never massive enough to reach the temperatures required for Carbon fusion.
This core must be under the Chandrasekhar limit of 1.4 solar masses. This is necessary, because the star’s shape is maintained, against the pull of gravity, by something called degeneracy pressure that would not be able to support a more massive star. (The more massive stars become black holes.)
The white dwarf maintains its same size as it cools (remember: degeneracy pressure is fighting gravity which wants to contract) but its luminosity and surface temperature decrease with time, tracking it further and further to the lower right hand corner of the HR diagram. And thus, it simply fades into obscurity.