As I've aged (I'm almost 41 now), I'm sure the same brilliant ideas surface from time to time, but I can't sift through the garbage anymore. I don't know if that's because the people have gotten worse, or whether I'm just getting more conservative as I age.
I'd say some big factors are:
It's more authentic than almost any other site. Moderators/janitors are pulled from the userbase, content is sourced directly from the users, and there isn't much behind the website beyond "we have stupid high amounts of traffic, let's get some ad revenue". The site is honest about what it is.
The site has a core feature set and doesn't do anything else. It's like Craigslist--it does one thing, and doesn't mess about with other things.
The site is remarkably uncensored, favoring containment boards. So, love it or hate it, 4chan is very free in the speech allowed. Everybody on the site knows the culture of whatever boards they visit, and there is a culture of mockery for people who are too thin-skinned. The flip side of this is that content that people really don't want to see (furry stuff, political stuff, etc.) has a clear place to go. This is the best strategy for that sort of work, since it keeps resentment from building up and makes it easy for users to avoid stuff they don't like.
Users feel empowered to enforce norms. Even using archaic tools, users feel directly responsible to call out ("sage") things that don't belong on their board. By contrast, a lot of sites have userbases who basically whine at mods and don't take responsibility for their culture.
The site has room for everybody, but it doesn't take itself seriously. There is a cooking board, a board for hardcore pornography, a board for papercraft and origami, a board for torrents, a board for animals, a board for nazis, a board for lgbtq+ folks...basically, there are clear communities available for everybody. And every board makes fun of itself.
Users are anonymous and posts go away. This is the one that always gets brought up, but the fact is that by having ephemeral accounts and posts, people are free to speak their mind and to change their position later without ill effect.
Just a technical note, I believe this is not true. AFAIK only janitors are recruited from users, the moderators (those with real power) were all personal friends of m00t (at least not so long ago). Maybe it changed since hiroyuki took over, but I have not read anything about it.
This. I'd also add the lack of "upvoting."
It's also not necessarily the most "uncensored", several such clones were famously a lot more open in certain discussions despite being effectively dead.
And finally it's not totally ephemeral these days, with several mirrors showing up.
At some point, any social network continues operating due to its critical mass of users.