Winston's dreams are significant in that we learn about the past from Winston's dreams, we learn about Winston's character, and we get some insight into Winston's future.
Some of Winston's dreams are about his childhood, before the Revolution and formation of the Party. Winston dreams of his mother and little sister. We learn how they disappeared during the Great Purges. We also see how little Winston thought of either one at the time and how much he misses those familial feelings now.
Winston also dreams of the Golden Country and he has a dream in which someone whispers to him, "We will meet in the place where there is no darkness." Winston, at first, believes this place to represent some kind of freedom from the Party. This dream actually foreshadows the events that ensue in the Ministry of Love, which is the place where there is no darkness and he learns that the voice in his dreams belonged to his torturer O'Brien.