A black dwarf star is a white dwarf star that has cooled down to the same temperature as the cosmic microwave background. The cosmic microwave background is the thermal radiation left over from the Big Bang or the temperature of the space around the star.
Once a star becomes a white dwarf, it no longer has an internal source of heat and is only still shining due to residual heat. Just like food taken out of an oven, it slowly cools. It first becomes a red dwarf, then a brown dwarf and, eventually, a black dwarf.
Black dwarfs are entirely hypothetical unlike red, brown and white dwarfs. It would take a white dwarf longer to become a black dwarf than the universe has existed, so there are no black dwarfs in existence.