African-Americans invented cool as a stylistic defiance against racism during World War II. This is simply well-documented social, historical, and linguistic fact. To be cool in the 1940s referred to the ability to be relaxed in one's own style in any environment, an act of courage and mental strength for any Black person during the Jim Crow era. Whether meaning high praise ("Cool!"), vetting someone to others ("she's cool"), or referring to a relaxed state of mind ("I'm cool, man") -- our modern usages all began in jazz culture.
Oh, you don't gotta worry about him, he's one of us, he's cool.
That guy over there did the right thing, he's cool in my book.
She's not cool, better watch your back.
when u generally don’t care about the conversation so u reply with “cool.” it could also mean that you just completely hate the person and aren’t listening to anything they’re saying so you would therefore say “cool”.
person 1: “yeah, my grandma just died last night cause she got hit by an ice cream truck”
person 2: “cool”