Below is an artists conception of how a Binary system of a White Dwarf and its evolving companion might look:
As the second star expands, becoming a Red Giant, its outer atmosphere might become caught up and pulled into orbit around the White Dwarf! The material passes through the Lagrangian Point from one star to the next.
In the diagram above, you also see the accretion disk which has formed around the White Dwarf. This forms because the material falling onto the White Dwarf must conserve angular moment.
The Surface of the White Dwarf is VERY HOT and the gravitational pull VERY HIGH. The material from the Red Giant is rich in Hydrogen. If it falls to the surface of the White Dwarf, it will immediately set off a Thermo Nuclear Reaction.
If a little bit of mass falls onto the White Dwarf, we see a NOVA .
Many binary systems show re-occurring NOVA explosions.
However, if a LOT of mass falls on, or if the White Dwarf has been taking on more and more material, slowly, going off as a Nova again and again, it might SURPASS the Chandrasekhar Limit.
In this case, the ENTIRE WHITE DWARF WILL DISINTEGRATE as a SUPERNOVA!