There is a basic paradox about what being "cool" is, and it is easy to explain, easy to give examples, but, of course, hard to explain the substance of why cool is a paradox.
Take a cool person you know. (cool institutions, art forms, activities, and the like are also accepted). Write down some adjectives that describe that person. After you have written a number, you will find them falling into two categories. You might write about how they are suave, charismatic, charming, street smart, worldly, sophisticated, popular, energetic...all attributes that relate somehow to them being able to relate to people and the world easily. But you might have also mentioned that they are individualistic, rebellious, non-conformist, abrasive, reclusive, and sometimes obsessed with minutiae. After reading that list, I hope you are thinking about Prince, who is a pretty representative cool person in that he was charismatic enough to connect with people as the top musician of a decade---but also a somewhat ornery nerd who spent his time sequestered in a suburban office park obsessing over musical detail. Or maybe you are thinking of Bob Dylan, the voice of a generation who didn't like that generation and periodically cratered his career by making inaccessible junk. And we haven't even left Minnesota yet. The cool are stuck between the glitz and the grit. Take away the grit and you have a used-car salesman, back slapping, obsequious and everyone's friend. Take away the glitz and you have GG Allin, someone who is just anti-social. Neither of them is cool. Coolness lies somewhere in-between.
You might be objecting to parts of this. If you are, there is good chance you are British, or from somewhere even further away, like New York City. When I lived in Santiago de Chile, the biggest culture shock for me was that it was the first time I was around people from the Eastern United States and Europe. To many people from places like that, "cool" is a synonym with trendy, fashionable or (heavens forbid) chic. There was a bland literalness to what they thought "cool" was. To someone from a European country, flying to a fancy ski resort and spending money on expensive food at a "trendy" restaurant or wearing "designer" clothing might be thought of as equivalent to the American "cool". In part, it is because Europeans have no concept of irony: no ability to understand that society is a series of constructions, and that even when relating to those things, it is possible to take them non-literally, to think more about our attitude towards them, than the things themselves. A British girl once used the word "cheeky" to me in a Whatsapp Message, and it made me quit my job and then stare at some railroad tracks for about half an hour, wondering whether to throw myself in front of a train, because I couldn't comprehend how someone would be so fucking uncool to use the word "cheeky" unironically. Because "cheeky", a term almost completely used by the British, is about the style of defiance with no substance behind it, a gesture thrown out to show you are fashionable, but with no content. And this girl had studied jazz in Jazz, she should know better!
Now lets take a little detour around that last point because I mentioned two things: style and substance, and jazz. And Oakland. While cultural historians might debate the specifics, the basic idea of "cool" came from jazz musicians, and the African-American community in general, in the days before civil rights. "Cool" was a way to defy social structures in an oblique way, because defying them openly could be dangerous to livelihood and life. It spread in the post-World War II period to different groups who somehow wished to question the status quo but either feared to do so openly, or didn't have the tools to do so. Before people had the tools to publish their opposition openly, they had to communicate it through eccentricity and weirdness that was just oblique enough to be undetectable to the authorities...but obvious enough to those In The Know. So here is a gigantic key part of being cool that is lost on many people: coolness always has an emancipatory message behind it. That is the substance of coolness, it is somehow freeing. This is a point lost on so many people in places like Silicon Valley and London: it is not possible to disappear for the weekend, take lots of drugs, have lots of sex, then pop up back on Monday ready to uphold the status quo. That is why Burning Man is so fucking uncool. It was why the Fyre Festival, even before it fell apart, was uncool. But as an addendum to that, the substance of a cool person is never ideological. Ideologues who try to hijack what they imagine of as "cool" to push their ideology make their ideology look simplistic and uncool at the same time. There is a goal of emancipation behind every act of coolness, but what that goal is, is "never quite what appears on the surface, and is utterly inaccessible to obtuse and literal minds." It is totally acceptable, even necessary for cool people to work within the structures of established industries. It is okay for a popular tv show or style of music to never overtly state a political idea, or to state it in a roundabout fashion. That does not ruin its coolness. But lack of substance does, and will.
And some people might be objecting to me saying even this much. Can "Coolness" be explained, and if it could, could it be explained by user of minor internet forum Everything2.com? What right do I have to speak of coolness? Well, I got a 45 rpm recording of Wabash Cannonball by country singer Rusty Draper for 25 cents out of a bin the other day, and that is my fucking cred. You are welcome for the effort I've put into explaining the concept of "cool" to you.