When a star much like our sun reaches the end of its lifetime, it enters the red giant phase, becoming many times larger. Then the outer layers of gas dissapate into space. The remainder of the star shrinks down to a compact white dwarf, where it burns the last of its fuel. These dying stars can be some of the hottest bodies in space. Once there is nothing left to burn, the core cools down, and becomes a brown dwarf.
But, if the star is part of a binary star system, something else may happen. While at the white dwarf stage, its increased gravity will begin to pull gases off of its companion star. The gas will stream from the star to the white dwarf and will begin orbiting around the dwarf in a flat disk, called an accretion disk. As the gasses are pulled in closer by gravity, they heat up. Once the preassure and heat become so great, most of the accumulated gas will be expelled violently away. This explosion of light and matter is what we call a nova.
After the explosion, the process may not be over yet. The white dwarf will continue attracting gas from its companion star, and the nova process will repeat itself, maybe even hundreds more times, resulting in recurring novae. Only the lack of available gas, or a Type I supernova can stop the process.