Old English wif "woman," from Proto-Germanic *wiban (cf. Old Saxon, Old Frisian wif, Old Norse vif, Danish and Swedish viv, Middle Dutch, Dutch wijf, Old High German wib, German Weib), of uncertain origin. Dutch wijf now means, in slang, "girl, babe," having softened somewhat from earlier sense of "bitch."
Some proposed PIE roots include *weip- "to twist, turn, wrap," perhaps with sense of "veiled person" (see vibrate); or *ghwibh-, a proposed root meaning "shame," also "pudenda," but the only examples of it are wife and Tocharian (a lost IE language of central Asia) kwipe, kip "female pudenda."
The modern sense of "female spouse" began as a specialized sense in Old English; the general sense of "woman" is preserved in midwife, old wives' tale, etc. Middle English sense of "mistress of a household" survives in housewife; and later restricted sense of "tradeswoman of humble rank" in fishwife. Wife-swapping is attested from 1954.