Deflagration is a process of subsonic combustion that usually propagates through thermoconductivity (hot burning material heats next layer of cold material and ignites it). Deflagration is different from detonation which is supersonic and propagates through shock compression.
Deflagrations are easier to control than detonations, and better suited when the goal is to move an object (a bullet in a gun, or a piston in an engine) with the force of the expanding gas.
Typical examples of deflagrations are combustion of a gas-air mixture in a gas stove or a fuel-air mixture in an internal combustion engine, a rapid burning of a gunpowder in a firearm or pyrotechnic mixtures in fireworks.