In 1984, what does Winston's dream of the girl with dark hair symbolize?
I assume you are referring to the dream that Winston has at the beginning of Chapter 3 in this terrifying dystopian novel. What is important to realise is that this dream of Julia, the girl he has noticed and feels sexually attracted to, comes after a dream of his mother and sister just before it. The remembrance of his mother and sister has a profound impact on Winston because through it he realises that:
Tragedy, he perceived, belonged to the ancient time, to a time when there was still privacy, love, and friendship, and when the members of a family stood by one another without needing to know the reason.
However, today, Winston reflects, such tragedy or emotions would be impossible:
Such things, he saw, could not happen today. Today there were fear, hatred, and pain, but no dignity of emotion, no deep or complex sorrows.
Of course, we need to understand that in a sense, Winston is able to live the kind of life he wants to in his dreams, for such a life would be impossible in the world of Big Brother. It is then that he has his dream of Julia, which is profoundly sexual:
With what seemed a single movement she tore off her clothes and flung them disdainfully aside... What overwhelmed him in that instant was admiration for the gesture with which she had thrown her clothes aside. With its grace and carelessness it seemed to annihilate a whole culture, a whole system of thought, as though Big Brother and the Party and the Thought Police could all be swept into nothingness by a single movement of the arm.
What this dream celebrates and represents is Winston's desire to live life richly and in such a way that would eradicate the barriers and impediments that control and prevent such passion and humanness being expressed. The dream recognises the sheer power of humanity which of course the Party is implacably opposed to. What of course happens in the novel is that Winston acts on this desire to "live" in spite of the danger.