Etymology
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holiday (n.)
1500s, earlier haliday (c. 1200), from Old English haligdæg "holy day, consecrated day, religious anniversary; Sabbath," from halig "holy" (see holy) + dæg "day" (see day); in 14c. meaning both "religious festival" and "day of exemption from labor and recreation," but pronunciation and sense diverged 16c. As an adjective mid-15c. Happy holidays is from mid-19c., in British English, with reference to summer vacation from school. As a Christmastime greeting, by 1937, American English, in Camel cigarette ads.
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holiday (v.)
"to pass the holidays," 1869, from holiday (n.).
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Roman holiday (n.)

"occasion on which entertainment or profit is derived from injury or death of another," 1860, originally in reference to holidays for gladiatorial combat; the expression seems to be entirely traceable to an oft-quoted passage on a dying barbarian gladiator from the fourth canto (1818) of Byron's "Childe Harold's Pilgrimage":

But where his rude hut by the Danube lay
There were his young barbarians all at play,
There was their Dacian mother. He, their sire,
Butcher'd to make a Roman holiday!
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*agh- 
Proto-Indo-European root meaning "a day" (as a unit of time). The initial d- in Germanic is of obscure origin.

It forms all or part of: adays; Bundestag; daily; daisy; dawn; day; holiday; Reichstag; today.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dah "to burn," Lithuanian dagas "hot season," Old Prussian dagis "summer."
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vacation (n.)

late 14c., "freedom from obligations, leisure, release" (from some activity or occupation), from Old French vacacion "vacancy, vacant position" (14c.) and directly from Latin vacationem (nominative vacatio) "leisure, freedom, exemption, a being free from duty, immunity earned by service," noun of state from past-participle stem of vacare "be empty, free, or at leisure," from PIE *wak-, extended form of root *eue- "to leave, abandon, give out."

Meanings "state of being unoccupied," "process of vacating" in English are early 15c. Meaning "formal suspension of activity, time in which there is an intermission of usual employment" (in reference to schools, courts, etc.) is recorded from mid-15c. As the U.S. equivalent of what in Britain is called a holiday, it is attested from 1878.

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Yom Kippur 
Jewish holiday, 1854, from Mishnaic Hebrew yom kippur (in Biblical Hebrew, yom kippurim), literally "day of atonement," from yom "day" + kippur "atonement, expiation."
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festival (n.)
1580s, "a festal day, appointed day of festive celebration," short for festival day (late 14c.), from Old French festival (adj.) "suitable for a feast; solemn, magnificent, joyful, happy," and directly from Medieval Latin festivalis "of a church holiday," from festum "festival, holiday," neuter of festus "of a feast" (see feast (n.)). The English word returned to French 19c. in certain specialized senses.
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emmet (n.)
"ant," from Old English æmete (see ant), surviving as a dialect word in parts of England; also, according to OED, in Cornwall a colloquial name for holiday tourists.
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feast (v.)
c. 1300, "partake of a feast," from Old French fester "to feast, make merry; observe (a holiday)" (Modern French fêter), from feste "religious festival" (see feast (n.)). Related: Feasted; feasting.
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heortology (n.)
"study of religious feasts and calendars," 1881, from Greek heorte "a feast or festival, holiday," + -ology. The immediate source of the English word is in French or German. Related: Heortological (1880).
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