I see and hear two general slang usages of cool – one meaning great (illustrated by a and b below), and one meaning acceptable/okay (illustrated by c and d). The following are Dictionary.com's four (read: two) definitions of the slang cool:
14. Slang
a. great; fine; excellent: a real cool comic.
b. characterized by great facility; highly skilled or clever: cool maneuvers on the parallel bars.
c. socially adept: It's not cool to arrive at a party too early.
d. acceptable; satisfactory; okay: If you want to stay late, that's cool.
Why did cool come to mean great or acceptable? Also, can anyone find some early usages? The biggest clue I have is this (from Dictionary.com):
Slang use for "fashionable" is 1933, originally Black English, said to have been popularized in jazz circles by tenor saxophonist Lester Young.
Googling Lester Young 1933 "cool", etc., did not yield me any fruit.
Best Answer
The Oxford English Dictionary writes:
The first example they give is from the 1930s:
The entry refers to hot as a comparison--the main entry is "Characterized by intensity or energy, in a positive or neutral sense (cf. sense A. 9); exciting, fast, successful, etc." and the related sense is:
This is first noted from the 1800s:
So, it looks like cool developed to mean the same thing as the earlier slang hot in African American English. There is no explanation of why this occurred.