"liaison at a particular time, by prearrangement," 1885, gradually evolving from date (n.1) in its general sense of "appointment." The romantic sense is by 1890s. Meaning "person one has a date with" is by 1900. Date-rape is attested by 1973.
c. 1400, daten, "to mark (a document) with a date," also "to assign to or indicate a date" (of an event), from date (n.1). Meaning "to mark as old-fashioned" is from 1895. Intransitive sense of "to have a date" is by 1850.
early 14c., "a period or stretch of time, a season, an age;" mid-14c., "time when something happened or will happen," from Old French date (13c.) "date, day; time," from Medieval Latin data, noun use of fem. singular of Latin datus "given," past participle of dare "to give, grant, offer," from PIE root *do- "to give."
From late 14c. as "the part of a writing or inscription which specifies when it was done." The sense transfer from "given" to "time" is via the Roman convention of closing every article of correspondence by writing "given" and the day and month -- meaning perhaps "given to messenger" -- which led to data becoming a term for "the time (and place) stated." A Roman letter would include something along the lines of datum Romae pridie Kalendas Maias -- "given at Rome on the last day of April."
Out of date "no longer in vogue" is attested from c. 1600.
"fruit of the date-palm," c. 1300, from Old French date, from Old Provençal datil, from Latin dactylus, from Greek daktylos "date," originally "finger, toe." Said to be so called because of fancied resemblance between oblong fruit of the date palm and human digits, but some say it is from the resemblance of the plant's leaves to the palm of the hand. It's also possible that this sense of daktylos is a word from a Semitic source (compare Hebrew deqel, Aramaic diqla, Arabic daqal "date palm") that has been assimilated by folk-etymology to the Greek word for "finger." Date-palm is from 1837; the earlier word was date-tree (c. 1400).
"old-fashioned," 1900, past-participle adjective from date (v.1) in the "mark as old-fashioned" sense.