Middle English wif, wyf, from Old English wif (neuter) "woman, female, lady," also, but not especially, "wife," from Proto-Germanic *wīfa- (source also of 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 and disputed etymology, not found in Gothic.
Apparently felt as inadequate in its basic sense, leading to the more distinctive formation wifman (source of woman). Dutch wijf now means, in slang, "girl, babe," having softened somewhat from earlier sense of "bitch." The Modern German cognate (Weib) also tends to be slighting or derogatory; Middle High German wip in early medieval times was "woman, female person," vrouwe (Frau) being retained for "woman of gentle birth, lady;" but from c. 1200 wip "took on a common, almost vulgar tone that restricted its usage in certain circles" and largely has been displaced by Frau.
The more usual Indo-European word is represented in English by queen/quean. Words for "woman" also double for "wife" in some languages. Some proposed PIE roots for wife include *weip- "to twist, turn, wrap," perhaps with sense of "veiled person" (see vibrate); and more recently *ghwibh-, a proposed root meaning "shame," also "pudenda," but the only examples of it would be the Germanic words 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 the later restricted sense of "tradeswoman of humble rank" in fishwife. By 1883 as "passive partner in a homosexual couple." Wife-swapping is attested from 1954.