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.
1794, "unfruitful, futile," from Latin otiosus "having leisure or ease, unoccupied, idle, not busy" (source of French oiseux, Spanish ocioso, Italian otioso), from otium "leisure, free time, freedom from business," a word of unknown origin. Meaning "at leisure, idle" is recorded from 1850. Compare Latin phrase otium cum dignitate "leisure with dignity." Earlier adjective in English was otious "at ease" (1610s), and Middle English had noun otiosity (late 15c.).
c. 1200, from Old English æmettig, of persons, "at leisure, not occupied; unmarried" (senses now obsolete), also, of receptacles, "containing nothing," of places, "unoccupied," from æmetta "leisure."
Watkins explains it as from Proto-Germanic *e-mot-ja-, with a prefix of uncertain meaning + Germanic *mot- "ability, leisure," possibly from PIE root *med- "take appropriate measures." A sense evolution from "at leisure" to "containing nothing, unoccupied" is found in several languages, such as Modern Greek adeios "empty," originally "freedom from fear," from deios "fear." "The adj. adeios must have been applied first to persons who enjoyed freedom from duties, leisure, and so were unoccupied, whence it was extended to objects that were unoccupied" [Buck].
The -p- is a euphonic insertion. Of words, etc., "destitute of force or effect," mid-14c. Related: Emptier. The figurative sense of empty-nester is attested by 1960.
late 14c., "freedom from obligations, leisure, release" (from some activity or occupation), from Old French vacacion "vacancy, vacant position" (14c.) and directly from Latin vacationem (nominative vacatio) "leisure, freedom, exemption, a being free from duty, immunity earned by service," noun of state from past-participle stem of vacare "be empty, free, or at leisure," from PIE *wak-, extended form of root *eue- "to leave, abandon, give out."
Meanings "state of being unoccupied," "process of vacating" in English are early 15c. Meaning "formal suspension of activity, time in which there is an intermission of usual employment" (in reference to schools, courts, etc.) is recorded from mid-15c. As the U.S. equivalent of what in Britain is called a holiday, it is attested from 1878.
1640s, "act or process of setting free; state of being disengaged," from French désengagement, from desengager (see disengage). By 1701 as "freedom from engrossing occupation, leisure."
early 15c., negotiacioun, "a dealing with people, trafficking," from Old French negociacion "business, trade," and directly from Latin negotiationem (nominative negotiatio) "business, traffic," noun of action from past participle stem of negotiari "carry on business, do business, act as a banker," from negotium "a business, employment, occupation, affair (public or private)," also "difficulty, pains, trouble, labor," literally "lack of leisure," from neg- "not" (from PIE root *ne- "not") + otium "ease, leisure," a word of unknown origin.
The sense expansion from "doing business" to also include "bargaining" about anything took place in Latin. Meaning "mutual discussion and arrangement of the terms of a transaction or agreement" is from 1570s.