The writer's world is another way of saying; "The scene that is being set for the story to be told. Time, Location, Characters, Mood, Situation, etc.
For example, If you were telling a story about Dungeons and Dragons, perhaps you would mention that the main characters, Corlon, a Fighter and Esmerelda, a Sorceress are Trapped in a Dragon's Cave guarded by a Large one-eyed Cyclops and a Very Large Hungry Green Dragon. And so on.
