The Definition of Cool:

cool (kūl)

adj., cool·er, cool·est.

1. Neither warm nor very cold; moderately cold: fresh, cool water; a cool autumn evening.
2. Giving or suggesting relief from heat: a cool breeze; a cool blouse.
3. Marked by calm self-control: a cool negotiator.
4. Marked by indifference, disdain, or dislike; unfriendly or unresponsive: a cool greeting; was cool to the idea of higher taxes.
5. Of, relating to, or characteristic of colors, such as blue and green, that produce the impression of coolness.

SYNONYMS: cool, composed, collected, unruffled, nonchalant, imperturbable, detached. These adjectives indicate absence of excitement or discomposure in a person, especially in times of stress. Cool usually implies merely a high degree of self-control, but it may also indicate aloofness: “Keep strong, if possible. In any case, keep cool. Have unlimited patience” (B.H. Liddell Hart). “An honest hater is often a better fellow than a cool friend” (John Stuart Blackie). Composed implies serenity arising from self-discipline: The dancer was composed as she prepared for her recital. Collected suggests self-possession: The witness remained collected throughout the questioning. Unruffled emphasizes calm despite circumstances that might elicit agitation: “with contented mind and unruffled spirit” (Anthony Trollope). Nonchalant describes a casual manner that may suggest, sometimes misleadingly, a lack of interest or concern: He reacted to the news in a nonchalant manner. Imperturbable stresses unshakable calmness usually considered as an inherent trait: “A man … /Cool, and quite English, imperturbable” (Byron). Detached implies aloofness resulting either from lack of active concern or from resistance to emotional involvement: He sat through the service with a detached air.

The usage of cool as a general positive epithet or interjection has been part and parcel of English slang since World War II, and has even been borrowed into other languages, such as French and German. Originally this sense is a development from a Black English usage meaning “excellent, superlative,” first recorded in written English in the early 1930s. Jazz musicians who used the term are responsible for its popularization during the 1940s.