A professor's year off is named after a farming rule. Leviticus 25 tells the Israelites to leave their fields unplanted every seventh year, a sabbatical year for the land.
The word goes back to Hebrew shabbath, "day of rest," from shabath, "he rested." Greek turned it into sabbaton, with an adjective sabbatikos, "of the Sabbath." Latin made that sabbaticus, which became the English adjective.
English had Sabbath since Old English times, but the adjective came much later. Etymonline dates sabbatical to the 1590s, meaning "recurring in sevens or on every seventh." David Wilton at Wordorigins.org cites a 1599 treatise on reckoning years that mentions a "Sabbaticall yeare." From the 1640s the word could also mean "of or suitable for the Sabbath."
In the 1800s, Wilton writes, the idea of a year of study after six years of work spread among the clergy. The preacher Edward Irving wrote in an 1828 letter, "Next Sabbath is the first of my Sabbatical year."
Universities took it from there. Wilton says Harvard was the first North American institution to adopt such a system, though without using the word at first. A report by President Charles Eliot, dated January 1881, said the Corporation would "grant occasional leave of absence for one year on half-pay." Etymonline dates the practice at Harvard to 1880.
Cornell and Wellesley followed in 1886. The earliest known use of "sabbatical" for this academic leave, according to Wilton, comes from Wellesley that year. It described "THE SABBATICAL GRANT, adopted by Harvard College." Etymonline records the phrase sabbatical year in this sense by 1886.
The adjective then became a noun. Etymonline dates "a sabbatical," short for sabbatical year, to 1934. The word has since spread well beyond campuses, to any extended break from work.
Underneath, the word still carries the old pattern from Leviticus: six periods of work, then one of rest.