I encountered the term in the book "You Shall Know Our Velocity" by Dave Eggers. I give this book my highest possible recommendation, for what it's worth. I'll frame this writeup so that I can explain the term without giving anything away from the novel. Personally, I think that if I did summarise the scene from the book, it wouldn't detract from reading it at all, but some may feel differently.
The Fourth world, put simply, is the world of transience. This is akin, but not identical, to "Ukiyo" - 浮世 the "Floating World" in the sense that Ukiyo is detached from the ordinary cares of life, and is a twilight world. Ukiyo does not carry the connotation of travel or movement that Eggers imputes in his term, however.
When we are travelling, we are not of the place we find ourselves in, and we are said to be in "the Fourth World". Before I encountered this idea, I had begun a notebook that I only record in when I'm on a plane, train, boat, or automobile, or feel myself in transit. Over the years I've built up a strong sense of the change in state when I am moving more lightly and quickly on the planet, a fleetingness.