maybe if you explained their function and what benefit they bring to members, and their impact on the game we might know something about it? i've asked this before and these threads always end with a vague non explanation or "stop asking". it seems bizarre to me that players create these things but then they act and function entirely like any other randomly generated group. the most input i've been able to fathom so far is a handful of factions have their own megaships, and the only control they exert over those is picking a number of locations for it to jump to each week. again: great, but - why?
Happy to! Having thought this over briefly, I think it's primarily two things. I'll highlight two excellent examples of my point (Black Omega, and my faction, Newton's Fusiliers).
1) You can't imagine how cool it is to see the name of your faction in game on a ship, station, or system. In a small way you and your friends made a mark on Elite: Dangerous. It provides a sense of ownership and investment that you may not get by adopting a faction or working for someone else's. Most importantly though...
2) It's a vehicle for stories staring you and all your friends. How did you blaze your own trail? What did you do in Elite: Dangerous? What do you have to show for it? There are a lot of incredible minor factions out there with dozens of people doing all kinds of stuff. The mechanics of it are not all that difficult - you're just playing the game, and every way to play the game is supported by BGS work (yes, even PvP!).
Plus, going back to my first point, you can customize you faction to provide the kind of gameplay you want. The differences between say, a Federally Aligned Corporation, an Imperial Patronage, and a Independent Anarchy are very real. Plus it's yours! It's got your name on it! How cool is that?
So, two factions I like. First, Black Omega. Minor faction page:
https://inara.cz/galaxy-minorfaction/5443/ Wing page:
https://inara.cz/wing/574/
They role play a private military contractor that's not afraid of shady deals out in the Pegasi Sector. As one of the oldest groups in Elite, you can see how much success they've had. More importantly, it's made up of a bunch of lovely guys and gals who work together to create fun for themselves. Not only are they great Elite players, but also creative types that make some of the best Elite stories out there (some of their authors easily rival Drew Wagar). I've been lucky enough to participate in some of these stories (War! Rebellion! Drama!).
Now for my own, Newton's Fusiliers. Minor faction page:
https://inara.cz/galaxy-minorfaction/38329/ Wing page:
https://inara.cz/wing/1547/
Yeah, yeah, we've got a bad reputation for being murder hobos

but our BGS story has been a lot of fun for us and our friends. First, we moved into Coma because it was a great location for Engineers and dang if it ain't just pretty as all get out. Then we decided to jump into the BGS thing so our faction was added back in April. Little did we know this particular system is very important to an Empire PowerPlay group so they didn't let us have it without a fight. We got stomped the first go around, asked Frontier to move, they denied that, so we pulled up our bootstraps and got to work. We just took control of the system last week!
Let me tell you what, a lot of people laughed at us saying we'd never accomplish this. Yet here we are. Feels awesome (and y'all are welcome to visit! We've got a strict 'fire if fired upon' policy so yeah, we're not going to just murder you for no reason in our backyard. CGs on the other hand though...

).
Other great factions include Loren's Legion, the Chapterhouse of Inquisition, Prismatic Knights, and heck as much as it chagrins me to say it even EXO. All these groups create enormous amounts of fun for their members.
In the end, I'll say this. Elite is an amazing game and I know dozens of people who would agree with me. Player Minor Factions are a huge part of that. By playing the game (running missions, trade, exploration, smuggling, PvE combat, PvP combat, and anything I forgot) and doing a bit of organization (usually in Discord) you can make your mark on the game world
and create some really cool stories to tell your grandchildren.
And furthermore, all of this is true
as the game exists right now.
Hope that answers your question, and more importantly, inspires you to check out Player Minor Factions and the BGS game.