A deflagration is (among other things) the result of the triggering of low explosive. It, like its cousin the detonation, is a decomposition event; however, the 'trigger' for the decomposition is not shockwave but combustion. Despite this, a deflagration can be a quite violent event; in fact, firearms tend to rely on deflagration rather than detonation. If a deflagration is confined, it can raise the local pressure to a level which causes an explosive failure of containment. This is how bullets and firecrackers function. Passing a shock wave through black powder would have little effect, unless movement or destruction of the grains caused enough friction to ignite them. One reason for their reliance on deflagration is that the energy buildup of a deflagration can be much easier to predict and control than that of a detonation, and can be confined more easily due to a predictable and relatively slow buildup of force on the container (a gun barrel, a cartridge case, an engine cylinder, etc.)

Put more simply (I hope) a deflagration is an explosion in which the shockwave of the explosion reaches each part of the explosive before the reaction front, because the reaction front is travelling more slowly than the speed of sound in the substance.

Note that a substance which would normally deflagrate can be induced to detonate sometimes by changing the conditions. However, many events which are loosely called 'detonations' (gasoline in an engine, gunpowder in a cartridge) are actually deflagrations. Explosive events can (and do) exhibit both deflagration reactions and detonation reactions; there is a phenomenon called the Deflagration to Detonation Transition which describes how a deflagrating mass can in fact detonate from released energy building up. In addition, reactions involving complex and/or multiple reactants can exhibit both due to the different reactions taking place.