"one-twelfth part of a year; one of the twelve parts into which the calendar year is arbitrarily divided," Old English monað, from Proto-Germanic *menoth- (source also of Old Saxon manoth, Old Frisian monath, Middle Dutch manet, Dutch maand, Old High German manod, German Monat, Old Norse manaðr, Gothic menoþs "month"), which is related to *menon- "moon" (see moon (n.)). Originally the month was the interval between one new moon and the next (a sense attested from late Old English).
Its cognates mean only "month" in the Romance languages, but in Germanic they generally continue to do double duty. The development of the calendrical meaning for words from this root in Greek (mēn) and Latin (mensis) was accompanied by the creation of new words for "moon" (selēnē, luna). The phrase a month of Sundays "a very long time" is from 1832 (roughly 7 and a half months but never used literally).
1640s, "one who calculates, a reckoner, one whose occupation is to make arithmetical calculations," agent noun from compute (v.).
Meaning "calculating machine" (of any type) is from 1897; in modern use, "programmable digital electronic device for performing mathematical or logical operations," 1945 under this name (the thing itself was described by 1937 in a theoretical sense as Turing machine). ENIAC (1946) usually is considered the first.
Computer literacy is recorded from 1970; an attempt to establish computerate (adjective, on model of literate) in this sense in the early 1980s didn't catch on. Computerese "the jargon of programmers" is from 1960, as are computerize and computerization.
WASHINGTON (AP) — A New York Congressman says the use of computers to record personal data on individuals, such as their credit background, "is just frightening to me." [news article, March 17, 1968]
Earlier words for "one who calculates" include computator (c. 1600), from Latin computator; computist (late 14c.) "one skilled in calendrical or chronological reckoning."