A delay detonation device was a timer set to explode at a given time. It acted much like an auto-destruct.
In 2267, Captain James T. Kirk ordered Lieutenant Commander Montgomery Scott to rig up a thirty-second delay detonation device onto the badly damaged USS Constellation's impulse drive, which Kirk planned to activate when the ship was maneuvered near the maw of the "doomsday machine", an ancient weapon from outside the Milky Way Galaxy which threatened to destroy the densely populated Rigel system. Kirk shortly afterward initiated Scott's delay detonation device and was beamed back to the USS Enterprise seconds before the Constellation was destroyed, taking the doomsday machine with it. (TOS: "The Doomsday Machine")