1620s, "cavalry soldier carrying firearms," and thus capable of service either on horseback or on foot, from French dragon, probably so called for the guns they carried, from dragon "carbine, musket," because the guns "breathed fire" like dragons (see dragon). Also see -oon. For the sense evolution, compare musket.
"to compel by repeated threats or harassment," 1680s, literally "to force by the agency of dragoons" (which were used by the French kings to persecute Protestants), from dragoon (n.). Related: Dragooned; dragooning.