Carbon detonation or carbon deflagration is the violent reignition of thermonuclear fusion in a white dwarf star that was previously slowly cooling. It involves a runaway thermonuclear process which spreads through the white dwarf in a matter of seconds, producing a Type Ia supernova which releases an immense amount of energy as the star is blown apart. The carbon detonation/deflagration process leads to a supernova by a different route than the better known Type II (core-collapse) supernova (the Type II is caused by the cataclysmic explosion of the outer layers of a massive star as its core implodes).
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Carbon detonation in the context of Supernova remnant
A supernova remnant (SNR) is the structure resulting from the explosion of a star in a supernova. The supernova remnant is bounded by an expanding shock wave, and consists of ejected material expanding from the explosion, and the interstellar material it sweeps up and shocks along the way.
There are two common routes to a supernova: either a massive star may run out of fuel, ceasing to generate fusion energy in its core, and collapsing inward under the force of its own gravity to form a neutron star or a black hole; or a white dwarf star may accrete material from a companion star until it reaches a critical mass and undergoes a carbon detonation.