The secondary star Sirius B is a white dwarf. White dwarfs are extremely compact objects that represent the final state of a star like the Sun when it has exhausted its nuclear fuel. White dwarfs contain the mass of a normal star compressed down to the size of about the Earth. Thus, the density is extremely high - as much as a million grams per cubic centimeter.
White dwarfs have no nuclear fuel left, so they shine primarily form the heat left over in their interior from when they were normal stars producing energy by thermonuclear fusion. Sirus B was the first white dwarf discovered. They are generally not easy to see because their low surface areas mean that they have low luminosities.