In 1984 what is the significance of Winston's dreams about O'Brien and his sister and mother?
Chapters 2 and 3. His dream of O'Brien (shall meet in a place where there is no darkness), and his dreams of his sister and mother disappearing. Deconstruct each one: what are the underpinnings of these dreams? What are their deeper meanings?
As the book continues, we learn a little bit more about the circumstances surrounding the disappearance of Winston's mother and sister, and realize that he harbors long-held feelings of guilt and shame over his involvement in it. Growing up, he was a selfish boy, always taking more food than was his share, whining quite a bit, and treating his mother cruelly. Granted, he was merely hungry, starving even, but Winston still feels guilty about it. After one particularly nasty episode, his mother and sister disappear, and Winston can't help but feel it is his fault. So, in his dream, his mother and sister are in some sort of sinking ship, or well, where he knows that they are going to die or suffocate. And they are looking up at him, who is in the sunshine, safe, with accusation and knowledge in their eyes, knowledge that he won't save them. The part that really gets Winston is this:
"He was out in the light and air while they were being sucked down to death, and they were down there because he was up here. He knew it and they knew it, and he could see the knowledge in their faces."
This dream directly reflects the guilt and shame that Winston felt over treating them so horribly when they were alive, and the subconscious feeling that he was somehow responsible for their disappearance. He has no confirmation of this fact, but feels so horrible that he is sure he must have driven them away to their deaths somehow.
The dream with O'Brien represents Winston's deep-seated desire to find someone to connect to, who feels the same way as he does about the party. He hates the party, but feels alone and vulnerable in that hatred. He suspects that O'Brien might feel the same too, but isn't sure. In his dream, those hopes are played out, and O'Brien is a co-conspirator, a fellow-hater, and gives him the elusive lines, "we shall meet in a place where there is no darkness." Winston interprets that line with a sense of hope; he ties it to the Golden Country, which is a land of sunshine and beauty that also frequents his dreams, where the Party is gone and real life can truly begin. O'Brien haunting his dream, offering hopes of a better life with no sorrows all reflect his dreams of such a thing actually being able to exist.
I hope that those thoughts helped; good luck!