Stars (Judgements) are basically gods, they enforce their reality (Laws) in their territory. They communicate (Correspondence) with each other via giant space crabs (Messengers) who speak in burning magical runes (Correspondence Sigils). The bat people (Masters) used to work for the space crabs - I think. In Albion, the star was dead so the Empress moved in and got the Clockwork Sun (artificial star for artificial Law) built, ostensibly with a bomb supplied by the anarchists but that's actually a lie, not sure why tbh. Maybe her rule seems more legitimate if she killed the previous ruler. In the Reach, uh, there's the Verdance, which I'm not really sure what is - some kind of lovecraftian fungus god. Maybe it's a star, too. The Verdance got into an argument with a star and negotiated via crab, the Obelisk at the circus is a memorial of this agreement. I keep forgetting bits and pieces of the Traitor's Wood story, but I think it boils down to an envoy that went rogue and was punished for it. The Verdance really wants to get Percy Blythe there to... something. I used to have a theory, but I don't remember. Eleutheria was a binary star system, one of the stars got hoodwinked and was killed in a moment of vulnerability, at the instigation of a native of the mirror world where the snakes live (Parabola). This is the most lovecraftian stuff in the entire setting imo, Parabola is some creepy shit. The Parabolan got some devils - devils, btw, are servants of the stars - to rebel. Ok, so one of the suns dies, the other one (the Halved) goes nuts and starts working to end all Law - this would be a disaster and would also present an opening for Parabolans to enter into reality I think. Dream-snakes certainly don't exist, which is why they live in opposite land. If the Laws of reality are suspended, they might be able to live in reality despite technically not existing. The Parabolan is currently imprisoned. The thing in the Well of the Wolf might be one of ringleaders of the devils who rebelled, I'm not sure.
Blue Kingdom is the only territory still being actively ruled by a real star. Rubbery Men come from a place they lost. Is it destroyed? Is it missing? Either way, Axile is gone. The Storm that Speaks is what's left of what used to be the star-god of Albion. The Burrower is a star dragon - these entities do freelance work for stars. I have no fucking clue what the Waste-Waif is. No idea about the Guests.
This is all I can think of off the top of my head, I played a little bit of Fallen London but that game has no gameplay. It might even have negative gameplay. I'm still missing a lot, but with this you should have a working model of what's going on.