A white dwarf is formed when a star has burned all of its original hydrogen and helium fuel to elements such as carbon, nitrogen and oxygen. If the star doesn't have enough mass, the pressure at its center is too low to burn these elements further, and so it no longer produces heat.
It is, however, still hot from the earlier burning stages, so it still glows for a while until it cools down. It takes tens to hundreds of billions of years for it to cool down entirely, and the Universe hasn't been around that long--the oldest stars are between 10 and 20 billion years old. Therefore there are no black dwarfs yet, but there will be in the future.
Source: wikipedia, NASA