A white dwarf is a stellar remanent which consists of primarily carbon and oxygen or helium, and is too small in order to fuse thosthose to heavier elements and has too little hydrogen left so that there is no hydrogen shell burning anymore either.
It will end in a supernova type Ia when it exceeds the mass limit for a white dwarf of about 1.4 solar masses (the so-called Chandrasekhar limit) - the limit when it actually becomes heavy enough to start fusing the helium and/or carbon in its core - a. When it starts to exceed this limit due to accretion the fusion reaction which will onset so heavily that nothing will remain of the starwhite dwarf and we will see a supernova.
However, if a white dwarf below this mass limit accretes further hydrogen, e.g. from its companion in a multiple system, it will occasionally and usually periodically amass enough hydrogen in its atmosphere so that the hydrogen content is enough that it temporarily starts hydrogen shell burning; this event is then visible as a nova.
The exact physics are not trivial, and also not every detail is fully understood so far of every of these processes - especially as different systems and mechanisms might interact so that several effects can overlap.