good-day n.

Old English gōd (with a long "o") "excellent, fine; valuable; desirable, favorable, beneficial; full, entire, complete;" of abstractions, actions, etc., "beneficial, effective; righteous, pious;" of persons or souls, "righteous, pious, virtuous;" probably originally "having the right or desirable quality," from Proto-Germanic *gōda- "fitting, suitable" (source also of Old Frisian god, Old Saxon gōd, Old Norse goðr, Middle Dutch goed, Dutch goed, Old High German guot, German gut, Gothic goþs). A word of uncertain etymology, perhaps originally "fit, adequate, belonging together," from PIE root *ghedh- "to unite, be associated, suitable" (source also of Sanskrit gadh- "seize (booty)," Old Church Slavonic godu "favorable time," Russian godnyi "fit, suitable," Lithuanian goda "honor," Old English gædrian "to gather, to take up together").

Irregular comparative and superlative (better, best) reflect a widespread pattern in words for "good," as in Latin bonus, melior, optimus.

Sense of "kind, benevolent" is from late Old English in reference to persons or God, from mid-14c. of actions. Middle English sense of "holy" is preserved in Good Friday. That of "friendly, gracious" is from c. 1200. Meaning "fortunate, prosperous, favorable" was in late Old English. As an expression of satisfaction, from early 15c. Of persons, "skilled (at a profession or occupation), expert," in late Old English, now typically with at; in Middle English with of or to. Of children, "well-behaved," by 1690s. Of money, "not debased, standard as to value," from late 14c. From c. 1200 of numbers or quantities, "large, great," of time or distance, "long;" good while "a considerable time" is from c. 1300; good way "a great distance" is mid-15c.

Why then, can one desire too much of a good thing. ["As You Like It"]

As good as "practically, virtually" is from mid-14c.; to be good for "beneficial to" is from late 14c. To make good "repay (costs, expenses), atone for (a sin or an offense)" is from late 14c. To have a good mind "have an earnest desire" (to do something) is from c. 1500. Good deed, good works were in Old English as "an act of piety;" good deed specifically as "act of service to others" was reinforced early 20c. by Boy Scouting. Good turn is from c. 1400. Good sport, of persons, is from 1906. The good book "the Bible" attested from 1801, originally in missionary literature describing the language of conversion efforts in American Indian tribes. Good to go is attested from 1989.

Old English dæg "period during which the sun is above the horizon," also "lifetime, definite time of existence," from Proto-Germanic *dages- "day" (source also of Old Saxon, Middle Dutch, Dutch dag, Old Frisian di, dei, Old High German tag, German Tag, Old Norse dagr, Gothic dags), according to Watkins, from PIE root *agh- "a day."  He adds that the Germanic initial d- is "of obscure origin." But Boutkan says it is from PIE root *dhegh- "to burn" (see fever). Not considered to be related to Latin dies (which is from PIE root *dyeu- "to shine").

Meaning originally, in English, "the daylight hours;" it expanded to mean "the 24-hour period" in late Anglo-Saxon times. The day formerly began at sunset, hence Old English Wodnesniht was what we would call "Tuesday night." Names of the weekdays were not regularly capitalized in English until 17c.

From late 12c. as "a time period as distinguished from other time periods." Day-by-day "daily" is from late 14c.; all day "all the time" is from late 14c.  Day off "day away from work" is attested from 1883; day-tripper first recorded 1897. The days in nowadays, etc. is a relic of the Old English and Middle English use of the adverbial genitive.

All in a day's work "something unusual taken as routine" is by 1820. The nostalgic those were the days is attested by 1907. That'll be the day, expressing mild doubt following some boast or claim, is by 1941. To call it a day "stop working" is by 1919; earlier call it a half-day (1838). One of these days "at some day in the near future" is from late 15c. One of those days "a day of misfortune" is by 1936.

salutation in parting, also goodbye, good bye, good-by, 1590s, from godbwye (1570s), a contraction of God be with ye (late 14c.), influenced by good-day, good evening, etc. As a noun from 1570s. Intermediate forms in 16c. include God be wy you, God b'uy, God buoye, God buy, etc.