date (n.1) Look up date at Dictionary.com
"time," early 14c., 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" (cognates: Sanskrit dadati "gives," danam "offering, present;" Old Persian dadatuv "let him give," Old Church Slavonic dati "give," dani "tribute;" Latin donum "gift;" Greek didomi, didonai, "to give, offer," doron "gift;" Lithuanian duonis "gift," Old Irish dan "gift, endowment, talent," Welsh dawn "gift").

The Roman convention of closing every article of correspondence by writing "given" and the day and month -- meaning perhaps "given to messenger" -- 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."
date (n.3) Look up date at Dictionary.com
"liaison," 1885, gradually evolving from date (n.1) in its general sense of "appointment;" romantic sense by 1890s. Meaning "person one has a date with" is from 1925.
date (n.2) Look up date at Dictionary.com
the fruit, late 13c., from Old French date, from Old Provençal datil, from Latin dactylus, from Greek daktylos "date," originally "finger, toe;" so called because of fancied resemblance between oblong fruit of the date palm and human digits. Possibly from a Semitic source (compare Hebrew deqel, Aramaic diqla, Arabic daqal "date palm") and assimilated to the Greek word for "finger."
date (v.2) Look up date at Dictionary.com
"have a romantic liaison;" 1902, from date (n.3). Related: Dated; dating.
date (v.1) Look up date at Dictionary.com
"to mark (a document) with the date," late 14c., from date (n.1). Meaning "to assign to or indicate a date" (of an event) is from c.1400. Meaning "to mark as old-fashioned" is from 1895. Related: Dated; dating.