c. 1300 as an adverbial phrase, "completely, thoroughly, to the utmost degree," from out (adv.). Adjective usage is attested by 1813.

in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."

In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]

late 15c., "egress," from out (adj). From 1620s, "a being out" (of something), from out (adv.). From 1764 in politics as "the party which is out of office." From 1860 in the baseball sense "act of getting an opposing player out of active play." From 1919 as "means of escape; alibi."

Old English utian "expel, put out," from the source of out (adv.). It has been used in many specific senses over the years; the meaning "disclose to public view, reveal, make known" is by mid-14c.

Eufrosyne preyde Þat god schulde not outen hire to nowiht. ["Legendary of St. Euphrosyne," c. 1350]

Meaning "to expose as a closet homosexual" is first by 1990 (as an adjective meaning "openly avowing one's homosexuality" it dates from 1970s; see closet). To come out "declare oneself publicly as homosexual" is from 1968 and probably short for come out of the closet. Related: Outed; outing. Compare outen.

late Old English, "outer," from out (adv.). From mid-13c. as "that is or lies on the outside, exterior." Of a light or candle, "extinguished, no longer burning," c. 1300.  Sense of "no longer secret" is by 1713. Sense in baseball (1860) was earlier in cricket (1746). Meaning "unconscious" is attested from 1898, originally in boxing from the notion of "defeated ('out') by failing to rise within a 10-count." To be out on one's feet is from 1952. From 1966 as "unfashionable, not stylish, popular, or modern."

expressing motion or direction from within or from a central point, also removal from proper place or position, Old English ut "out, without, outside," from Proto-Germanic *ūt- (Old Norse, Old Frisian, Old Saxon, Gothic ut, Middle Dutch uut, Dutch uit, Old High German uz, German aus), from PIE root *uidh- "up, out, up away, on high" (source also of Sanskrit ut "up, out," uttarah "higher, upper, later, northern;" Avestan uz- "up, out," Old Irish ud- "out," Latin usque "all the way to, continuously, without interruption," Greek hysteros "the latter," Russian vy- "out").

Sense of "to a full end, completely, to a conclusion or finish" is from c. 1300. Meaning "so as to be no longer burning or alight; into darkness" is from c. 1400. Of position or situation, "beyond the bounds of, not within," early 15c. Meaning "into public notice" is from 1540s; that of "away from one's place of residence," c. 1600. The political sense of "not in office, removed or ejected from a position" is from c. 1600. Meaning "come into sight, become visible" (of stars, etc.) is by 1610s. In radio communication, a word indicating that the speaker has finished speaking, by 1950.

As a preposition, "out of; from, away from; outside of, beyond; except; without, lacking;" mid-13c., from the adverb.

Meaning "from harmonious relations, into quarreling" (as in to fall out) is from 1520s. Meaning "from one's normal state of mind" (as in put out) is from 1580s; out to lunch "insane" is student slang from 1955. Adjectival phrase out-of-the-way "remote, secluded" is attested from late 15c. Out-of-towner "one not from a certain place" is from 1911. Out of this world "excellent" is from 1938; out of sight "excellent, superior" is from 1891. To (verb) it out "bring to a finish" is from 1580s. Expression from here on out "henceforward" is by 1942. Out upon, expressing abhorrence or reproach, is from early 15c.

also handout, hand out, 1882, "alms or food given to a beggar," hobo slang, from the verbal phrase; see hand (v.) + out (adv.). Meaning "distributed printed informational matter" is from 1927.

also dropout, "one who 'drops out' of something" (a course of education, life, etc.), 1930, from the verbal phrase drop out "withdraw or disappear from place" (1550s); see drop (v.) + out (adv.). 

also holdout, one who abstains or refrains when others do not, by 1911, from verbal expression hold out, which is attested from 1907 in the sense "keep back, detain, withhold" (see hold (v.) + out (adv.)). Earlier as the name of a card-sharper's device (1893). The verbal phrase is attested from 1520s as "stretch forth," 1580s as "resist pressure."

also blowout, 1825, American English colloquial, "outburst, brouhaha" (what in modern vernacular would be called a blow-up), from the verbal phrase, in reference to pressure in a steam engine, etc., from blow (v.1) + out (adv.). The meaning "abundant feast" is recorded from 1824; that of "a bursting of an automobile tire" is from 1908.