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]
distance n.
c. 1300, distaunce, "a dispute or controversy, civil strife, rebellion;" early 14c., "disagreement, discord, strife;" from Old French destance "discord, quarrel" (13c.), with later senses directly from Latin distantia "a standing apart," from distantem (nominative distans) "standing apart, separate, distant," present participle of distare "stand apart," from dis- "apart, off" (see dis-) + stare "to stand," from PIE root *sta- "to stand, make or be firm."
Meaning "remoteness of space, extent of space between two objects or places" is from late 14c. Also "an interval of time" (late 14c., originally distaunce of times). Meaning "remote part of a field of vision" is by 1813. The figurative sense of "aloofness, remoteness in personal intercourse" (1590s) is the same as in stand-offish.
At a distance "far away" is from 1650s. To keep (one's) distance was originally figurative (c. 1600). Phrase go the distance (1930s) seems to be originally from the prize ring, where the word meant "scheduled length of a bout." But it also was a term in 19c. horse-racing heats, where distance meant "the space behind the winning horse in a race that other competing horses must be inside to avoid being disqualified for subsequent heats."