Close readings reveal dramatic differences between the book's setting and our world that aren't at all apparent if you rush through the books. The protagonist refers to his pet as a dog, but reading his descriptions of the creature closely you might realize his definition of a dog is very different from our own. At another point in the story, the protagonist has a vision of a blue sky and describes it as incomprehensibly bright, indicating that the sun has dimmed and the planet is stuck in a sort of perpetual twilight.
Once the reader notices these things, they might start to realize just how different the setting of the book is. Suddenly everything in the text is open to interpretation. At one point you realize that people who operate spaceships in this setting are referred to as sailors. Does that mean all of the other 'sailors' that Severian encountered previously are actually interstellar travelers? What about the character who spoke with a sailor's accent? Was that horse that Severian rode an actual horse, or some far-future alien analog? Many of these moments are very brief and easy to miss - the book doesn't take time to explain or emphasize this divergent use of language. You can read this book over and over and still get something new out of it.