One dream sequence that establishes crucial background information is Winston's dream about O'Brien, described in Chapter Two. Walking through a darkened room, Winston dreams that he hears O'Brien's voice saying "We shall meet in the place where there is no darkness." This provides background for Winston's obsession with O'Brien, based on a fantasy that he is somehow also a dissident from the Party. This obsession eventually has dire consequences for Winston and Julia.
Another example is in Chapter three, when his mother appears in his dream holding his young sister. The two of them are first at the bottom of a well and then inside a ship that appears to be sinking. Winston somehow knows (though we can't be sure why) that his mother's death is his fault, but that his mother doesn't blame him for it. The dream suggests that Winston has experienced extreme turmoil, and that the Party's rise to power destroyed his family. This establishes important background details, both about Winston's life and about the way the Party came to control England.