"outer border, section or part that 'skirts' along the edge or boundary," 1590s, from out- + skirt (n.) in its secondary sense of "edge, border." Now only in plural, outskirts; originally in Spenser, and singular.
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]
early 14c., "lower part of a woman's dress," from Old Norse skyrta "shirt, a kind of kirtle;" see shirt. Sense development from "shirt" to "skirt" is possibly related to the long shirts of peasant garb (compare Low German cognate Schört, in some dialects "woman's gown"). Sense of "border, edge" (in outskirts, etc.) first recorded late 15c. Metonymic use for "women collectively" is from 1550s; slang sense of "young woman" is from 1906; skirt-chaser first attested 1942.