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Out of date "no longer in vogue" is attested from c. 1600.