active word-forming element in English and in many verbs inherited from French and Latin, from Latin de "down, down from, from, off; concerning" (see de), also used as a prefix in Latin, usually meaning "down, off, away, from among, down from," but also "down to the bottom, totally" hence "completely" (intensive or completive), which is its sense in many English words.
As a Latin prefix it also had the function of undoing or reversing a verb's action, and hence it came to be used as a pure privative — "not, do the opposite of, undo" — which is its primary function as a living prefix in English, as in defrost (1895), defuse (1943), de-escalate (1964), etc. In some cases, a reduced form of dis-.
"thick, obscuring mist," 1540s, a back-formation from foggy (which appeared about the same time) or from a Scandinavian source akin to Danish fog "spray, shower, snowdrift," Old Norse fjuk "drifting snow storm." Compare also Old English fuht, Dutch vocht, German Feucht "damp, moist." Figurative phrase in a fog "at a loss what to do" first recorded c. 1600. Fog-lights is from 1962.