late 14c., "waste parts, refuse," especially the waste meat and entrails of a bird or animal used as food, from off (prep.) + fall (v.). The notion is "that which is allowed to 'fall off' the butcher's block as being of little use. Compare Middle Dutch afval, German abfall "waste, rubbish." Also compare English offcorn (mid-14c.) "refuse left after winnowing grain," offcast (late 14c.) "parts of plants normally uneaten." As verbs, Middle English had offhew, offhurl, offshred, offsmite.
Old English fællan (Mercian), fyllan (West Saxon) "make fall, cause to fall," also "strike down, demolish, kill," from Proto-Germanic *falljanan "strike down, cause to fall" (source also of Old Frisian falla, Old Saxon fellian, Dutch fellen, Old High German fellen, German fällen, Old Norse fella, Danish fælde), causative of *fallanan (source of Old English feallan; see fall (v.)), showing i-mutation. Related: Felled; feller; felling.
Old English hærfest "autumn," as one of the four seasons, "period between August and November," from Proto-Germanic *harbitas (source also of Old Saxon hervist, Old Frisian and Dutch herfst, German Herbst "autumn," Old Norse haust "harvest"), from PIE root *kerp- "to gather, pluck, harvest."
In Old English and Middle English it was primarily a season name, with only an implied reference to the gathering of crops. The meaning "the time of gathering crops" is attested by mid-13c., and the sense was extended to the action itself and the product of the action (after c. 1300). After c. 1500 these were the main senses and the borrowed autumn and repurposed fall (n.) supplied the season name.
The figurative uses begin by 1530s. As an adjective, from late 14c. Harvest home (1570s) was a festive celebration of the bringing home the last of the harvest; harvest moon (1704) is that which is full within a fortnight of the autumnal equinox.
1560s, "exactly corresponding, having the same nature or character;" 1590s, "happening at the same time, concurrent," from French coincident, from coincider,from Medieval Latin coincidere, literally "to fall upon together," from assimilated form of Latin com "with, together" (see com-) + incidere "to fall upon" (from in- "upon" + combining form of cadere "to fall," from PIE root *kad- "to fall").
1725, American English, "fall of water" (earlier shoot, 1610s), from French chute "fall," from Old French cheoite "a fall," fem. past participle of cheoir "to fall," from Latin cadere"to fall," from PIE root *kad- "to fall." Meaning "inclined tube, trough" is from 1804; that of "narrow passage for cattle, etc." first recorded 1871. In North America, absorbing some senses of similar-sounding shoot (n.1).
"relapsed criminal," 1863, from French legal term récidiviste (by 1847), from récidiver "to fall back, relapse," from Medieval Latin recidivare "to relapse into sin," from Latin recidivus "falling back," from recidere "fall back," from re- "back, again" (see re-) + combining form of cadere "to fall" (from PIE root *kad- "to fall"). As an adjective by 1883.