The cartel is a meme in itself. But at this point /a/ has so many newfags that they don't remember it was originally a tongue-in-cheek joke. Basically there's this group of fansubbers dating back to the 00s who organized out of various IRC channels, but mainly ones like #news and later #intel. These groups shared staff members with each other, followed similar style guides, and enforced uniform quality of releases between themselves. Fansubbing groups that were a part of this were Commie, FFF, Underwater, etc.
At the time, fansubbing was the main way people watched seasonal anime. Simulcasts were nonexistent, so if you wanted to watch the newest show in Japan you had to have a fansubber sub it for you. This group of fansubbers thus controlled access to anime for a lot of people, between their various groups they picked up a ton of shows. So that's the first major influence they had. The second is many of the cartel's senior members were moderators on the original NyaaTorrents, which was the largest public anime torrent tracker on the internet. If you were a fansubber you had to go through Nyaa if you wanted any serious traffic for your releases, and the cartel had the power to ban people from that tracker if they upset them (though it basically never happened). They could also tag and rate releases according to their own standards, allowing them to enforce their own guidelines onto other groups outside their clique. Probably the most notorious example of this is when Daiz (an encoder who used to run a fansub group, also was a mod on NT) decided to shift the fansubbing encode standard to 10bit from 8bit. Even though only the groups affiliated with him did it at first, that was still a lot of anime suddenly only available in 10bit at a time when most people did not have players capable of playing 10bit video. Hence a lot of butthurt on /a/ over Daiz "holding their anime hostage" and other such nonsense. That's what I think really started the cartel meme in earnest.
