Especially "opportunity afforded by freedom from necessary occupations" (late 14c.). "In Fr. the word has undergone much the same development of sense as in Eng." [OED]. The -u- appeared 16c., probably on analogy of pleasure (n.), etc. To do something at leisure "without haste, with deliberation" (late 14c.) preserves the older sense. To do something at (one's) leisure "when one has time" is from mid-15c.
Old English tima "limited space of time," from Proto-Germanic *timon- "time" (source also of Old Norse timi "time, proper time," Swedish timme "an hour"), from PIE *di-mon-, suffixed form of root *da- "to divide."
Abstract sense of "time as an indefinite continuous duration" is recorded from late 14c. Personified at least since 1509 as an aged bald man (but with a forelock) carrying a scythe and an hour-glass. In English, a single word encompasses time as "extent" and "point" (French temps/fois, German zeit/mal) as well as "hour" (as in "what time is it?" compare French heure, German Uhr). Extended senses such as "occasion," "the right time," "leisure," or times (v.) "multiplied by" developed in Old and Middle English, probably as a natural outgrowth of such phrases as "He commends her a hundred times to God" (Old French La comande a Deu cent foiz).
to have a good time ( = a time of enjoyment) was common in Eng. from c 1520 to c 1688; it was app. retained in America, whence readopted in Britain in 19th c. [OED]
Time of day (now mainly preserved in negation, i.e. what someone won't give you if he doesn't like you) was a popular 17c. salutation (as in "Good time of day vnto your Royall Grace," "Richard III," I.iii.18), hence to give (one) the time of day "greet socially" (1590s); earlier was give good day (mid-14c.).
The times "the current age" is from 1590s. Behind the times "old-fashioned" is recorded from 1831. Times as the name of a newspaper dates from 1788. To be ahead of (one's) time is by 1837.
Time warp is attested by 1954; time-traveling in the science fiction sense is by 1895 in H.G. Wells' "The Time Machine." Time capsule is attested from 1938, in reference to the one "deemed capable of resisting the effects of time for five thousand years preserving an account of universal achievements embedded in the grounds of the New York World's fair."
Jones [archaeologist of A.D. 5139] potters about for a while in the region which we have come to regard as New York, finds countless ruins, but little of interest to the historian except a calcified direction sheet to something called a "Time Capsule." Jones finds the capsule but cannot open it, and decides, after considerable prying at the lid, that it is merely evidence of an archaic tribal ceremony called a "publicity gag" of which he has already found many examples. [Princeton Alumni Weekly, April 14, 1939]
To do time "serve a prison sentence" is from 1865. Time frame is attested by 1964; time-limit is from 1880. About time, ironically for "long past due time," is recorded from 1920. To be on time is by 1854 in railroading.