day (n.)

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.

Definitions of day
day (n.)
time for Earth to make a complete rotation on its axis;
they put on two performances every day
two days later they left
there are 30,000 passengers per day
Synonyms: twenty-four hours / twenty-four hour period / -hour interval / solar day / mean solar day
day (n.)
some point or period in time;
these days it is not unusual
after that day she never trusted him again
it should arrive any day now
those were the days
day (n.)
a day assigned to a particular purpose or observance;
day (n.)
the time after sunrise and before sunset while it is light outside;
the dawn turned night into day
Synonyms: daytime / daylight
day (n.)
the recurring hours when you are not sleeping (especially those when you are working);
my day began early this morning
it was a busy day on the stock exchange
she called it a day and went to bed
day (n.)
an era of existence or influence;
in the day of the dinosaurs
he was a successful pianist in his day
in the days of the Roman Empire
in the days of sailing ships
day (n.)
the period of time taken by a particular planet (e.g. Mars) to make a complete rotation on its axis;
how long is a day on Jupiter?
day (n.)
the time for one complete rotation of the earth relative to a particular star, about 4 minutes shorter than a mean solar day;
Synonyms: sidereal day
day (n.)
a period of opportunity;
every dog has his day
he deserves his day in court
Day (n.)
United States writer best known for his autobiographical works (1874-1935);
Synonyms: Clarence Day / Clarence Shepard Day Jr.