A good question, and I’ll need to go a bit deeper on this than usual! Sorry if the answer ends up being very long.
So a cataclysmic variable is a binary system with 2 stars in it. The main star, which we call the primary star, is a white dwarf – which means it isn’t burning any elements. It’s just a sphere of elements (mainly oxygen and neon in the core, and a layer of hydrogen and helium on the surface) hanging around doing nothing. It’s mass is typically about 0.8 times the mass of the Sun, and it’s size is about the size of the Earth (so it’s very very dense).
The second star is very similar to our own Sun – it’s about 0.24 times the mass of the Sun, and burns hydrogen in its core.
The white dwarf is dense enough and close enough to the second star that it strips material off of the second star. All that material forms what we call an accretion disk, and it’s mainly hydrogen. Eventually, that hydrogen ends up on the surface of the white dwarf, where it doesn’t do much. (Here’s an artists impression of one of these systems. The blue object is the white dwarf and the red one is the second star http://www.space-art.co.uk/image.php?gallery=stars-nebulae&image=intermediate-polar-binary )
Until, that is, enough hydrogen has fallen onto the surface of the white dwarf that the entire layer of hydrogen fuses in a matter of seconds, which is when the system explodes!
Then, the system settles back down again, and repeats this process! Here’s a graph showing how often it happens
Every time the graph goes up is an explosion, followed by the system relaxing again.
I study them because cataclysmic variables are used to probe the Universe – since we know what they look like when they blow up, we can figure out how far away a system is by comparing the observed explosion to our models. This was used to discover that our Universe was expanding at an accelerating rate, and was awarded the Nobel Prize in Physics in 2011!