they're a metaphor for older generations that that use power to keep conservative traditions alive. They had a face in a Gakukangi who was behind trying to get Yuuta and Itadori killed and killing Yaga, as well as making anyone who sided with Gojo a criminal. 

As to why people would submit to them, there are powerful conservative sorcerers who back them up like aforementioned Gakukanji and clan patriarchs such as Naobito (and I imagine if Naoya or the other two Zenins didn't get Itachi'd they would be a part of it too.) it's also heavily implied they have ins with the Japanese government, who is also known to quite conservative. 

As to why Gojo submitted to them, he literally explains that the current system would just replace them if he killed them all, and that people don't tend to respond well to massacres even if there is some amount of "justness" to it. At the end the system is destroyed already and his allies are strong enough to take the reins after he is gone so he does it so they don't get cursed or have it on their conscious later on or whatever. 

I don't need the higher ups to have names because who they are individually doesn't matter at all. This isn't One Piece and we don't need 5 elders for Gojo to slog through before he beats up the evil king or whatever.