A white dwarf is a star that is very small and dense. To give you an idea of how dense a white dwarf is for its size, its mass would be as great as our sun's but its size would be closer to that of Earth's. Only neutron stars and black holes are more dense than white dwarfs.
A white dwarf is one of the last stages of a star's life. Usually, smaller stars will eventually turn into white dwarfs while larger stars will turn into neutron stars or black holes. As a red giant's outer layers shed off into planetary nebula, eventually only a core of carbon and oxygen is left behind. This is the white dwarf. Although initially extremely hot, white dwarfs loose their light intensity and heat over billions of years until they become a black dwarf (the theoretical end to a white dwarf's life), a stage at which they no longer produce their own heat or light.