A white dwarf is a a star supported by electron degeneracy. It is the final fate of a star of the mass of the sun, after the red giant phase. The density of a white dwarf is very high: a white dwarf with the mass of the sun is about the size of the earth. The higher the mass of the white dwarf, the smaller the size. There is an upper limit to the mass of a white dwarf, the Chandrasekar limit, after which the pressure of the electrons is no longer able to balance gravity, and the star continues to contract, eventually forming a neutron star.
White dwarf stars are extremely hot, hence the bright white light they emit. This heat is a remnant of that generated from the star's collapse, and is not being replenished, but since white dwarfs have an extremely small surface area from which to radiate this heat energy they remain hot for a long period of time. Eventually a white dwarf will cool into a black dwarf, but the universe has not existed long enough for any white dwarfs to have had enough time to cool down this far yet and so no black dwarfs are thought to exist.
White Dwarf is also the name of a magazine.