I'm confused about the wakings, and the dreaming, and the city and everything--what's the short answer?

The short answer is that Eidolon City isn't real, but the people living in Eidolon City don't know that. Eidolon City is an illusion - albeit an all singing, all dancing, very real seeming illusion. Some people (known as Wakings) in Eidolon City can have limited access to the real world, but this access they experience as dreams - so, when they sleep in Eidolon City, they sometimes dream of the real world and what is happening in it.
So!
The Dream = the real world
Eidolon City = collective illusion