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Detonation, the word associated with the ignition of explosives, means the spread of a material's ignition by a shock wave, the shock wave's heating-effect producing the necessary temperature to ignite further material. In contrast is deflagration in which ignition occurs merely from proximity to the heat of existing fire, such as from conduction of heat. A difference is that detonation expands supersonically whereas deflagration is subsonic.
In astrophysics, the words are generally used in relation to fusion (rearrangement of nucleons forming new nuclei) rather than typical (chemical) burning (rearrangement of the bonding of atoms forming new molecules), but the mathematical models of the manner in which ignition spreads have much in common.
The occurrence and mechanism of deflagration to detonation transitions (DDTs) are of interest both for chemical explosions and for nuclear explosions (such as novae and Type Ia supernovae) and are of special interest regarding the Type Ia supernova problem.
Note that the abbreviation DDT is also seen in astrophysics for director's discretionary time.