copy of Goldstein's book. The fact that Winston is the one who utters this phrase is indicative of his optimism. Winston thinks that O'Brien has recognised "thisallusion" but it is doubtful that he has. It is more likely that he played along to encourage Winston in his anti-party activities.

Ironically, O'Brien is not the man Winston believes him to be; he is a member of the Thought Police and "the place in which there is no darkness," is, in fact, the Ministry of Love, and is a symbol of Winston's torture and reintegration into society. Just like the party's ironic slogans, like War is Peace, irony is at the very heart of 1984and defines the course of Winston's life. 

As indicated in the response above, the quote appeared several times throughout the novel. The very first instance was when Winston recalled a dream he had had seven years back in which a voice of someone seated next to him in a pitch dark room spoke the words to him. Even though Winston was certain that it was O’Brien that spoke to him, he was unsure whether his dream occurred before or after he saw O’Brien for the first time. Winston thought of these words on several occasions and did not know what they meant exactly. He thought that they referred to a future time in which people would live free of control by the Party. Darkness signifies the bondage in terms of thought and action that the people live through under the Party’s control.

The only time these words were actually spoken out was during Winston’s visit to O’Brien’s house. As he bid O’Brien goodbye, Winston said the words to which O’Brien responded with the same phrase as if cognizant of what it meant. Later on while undergoing torture in the hands of O’Brien at the Ministry of Love, it struck Winston that this was the place O’Brien meant they would meet and not a hopeful future as Winston has supposed. At the Ministry of Love, the light in the windowless room were never switched off and they resembled day light.

This quote is important because it represents hope for a better future.

This quote occurs a number of times in the book.  In the only times when we know for sure who is saying it, O'Brien is saying it.  It is sort of a mantra of the supposed resistance against the Party.  Because it is a mantra of resistance, it becomes something of a comfort and a goal to Winston.

Winston hopes, throughout the book, for the day when people will be able to meet in a place where there is no darkness.

He knew what it meant, or thought he knew. The place where there is no darkness was the imagined future...

He takes this to mean a place where there is no longer the sort of control of people that the Party now has -- a place where people can actually let their thoughts and feelings out into the light.

The quotation "a place where there is no darkness" occurs twice in George Orwell's "1984."  That is certainly no accident, given Orwell's writing style and his portrayal of life in a totalitarian society.

In a totalitarian society, especially as portrayed by Orwell, there is no freedom save of one's personal thoughts -- and those are communicated to others at risk of imprisonment or death.  Dreams, therefore, represent an escape from the constant repressiveness of the society in which Winston Smith lives.  Only through his dreams can Winston reflect on the past and entertain thoughts of the future.  When, in a dream, Winston's future torturer O'Brien states that "we shall meet in a place where is no darkness," it can mean multiple things.  First is the sanctity of the dream-state, into which the government cannot peek.  Darkness in the context of Orwell's use of this phrase refers both to the emergence of a free society where repression, indoctrination, and omniscient surveillance are no longer the defining characteristics of society, and to the lighted prison cell into which no darkness is permitted, lest the prisoner be allowed to sleep.  Constant light is a form of psychological torture routinely used even today, as it is an essential component of the use of sleep deprivation as a means of "breaking" a prisoner.  In other words, "where there is no darkness" denotes both freedom and repression, depending upon the context.

The dual-meaning of the phrase "where there is no darkness" is consistent with the underlying theme of "1984" and the use of "doublespeak."  The notion of "thought police," a central component of Orwell's story, speaks to the importance of dream sequences throughout the book, and that, combined with "doublespeak," provide the context from which Winston's dream about a conversation with O'Brien -- a conversation the content of which would get him imprisoned -- is born.

[as a side note/recommendation, the 2006 German film "The Lives of Others" captures the essence of the totalitarian society and the emergening conscience of a "Winston" quite well.]