When a white dwarf has a close companion star, the companion will often begin to have its outer atmosphere drawn away from it by the white dwarf's gravity as the companion star ages and expands into a red giant. The gasses so captured consist primarily of hydrogen and helium, the two principle constituents of matter in the universe. The gasses are compacted on the white dwarf's surface by its enormous gravity, compressed and heated to enormous temperatures as additional material is drawn in. Eventually, the pressures and temperatures within the hydrogen layer becomes great enough to trigger a nuclear fusion reaction that rapidly converts a large amount of the hydrogen into helium and other heavier elements.
The enormous amount of energy liberated by this process blows the remaining gasses off of the white dwarf's surface and produces an extremely bright but brief-lived outburst of light. This bright light, lasting only a matter of days, gave rise to the name nova, which is latin for "new"; ancient astronomers would see a nova become visible in the night sky where no star was visible before, and believed that it was a "new star."
A white dwarf can potentially generate multiple novae over time as additional hydrogen continues to accrete onto its surface from its companion star. Eventually, however, either the companion star will either run out of material, or the white dwarf will undergo a nova so powerful that it is completely destroyed in the process. This is somewhat similar to a type Ia supernova. Supernovae in general, however, involve different processes as well as much higher energies, and should not be confused with ordinary novae.