Syme is one of the more interesting minor characters in the novel. Winston likes to talk to him because Syme is working on refining Newspeak and can converse intelligently about it. In fact, Winston realizes, Syme's insightfulness will be his own undoing. As Syme chats to Winston over lunch at work, it strikes Winston that:

One of these days, thought Winston with sudden deep conviction, Syme will be vaporized. He is too intelligent. He sees too clearly and speaks too plainly. The Party does not like such people.

Not long after the lunch conversation, Syme disappears, as Winston had predicted:

Syme had ceased to exist: he had never existed

When O'Brien stops Winston in the hall to talk him and ask him to come to his apartment to get an advance copy of the latest Newspeak dictionary, Winston is certain O'Brien is referring to Syme when he mentions a "friend:"

"But you write it very elegantly," said O’Brien. "That is not only my own opinion. I was talking recently to a friend of yours who is certainly an expert. His name has slipped my memory for the moment."

Winston analyses O'Brien's words as follows:

It was inconceivable that this was anything other than a reference to Syme. But Syme was not only dead, he was abolished, an unperson. Any identifiable reference to him would have been mortally dangerous. O’Brien’s remark must obviously have been intended as a signal, a codeword. By sharing a small act of thoughtcrime he had turned the two of them into accomplices.

This is ironic because O'Brien never utters Syme's name. Winston simply jumps to the conclusion that he must be referring to Syme, and from there he weaves an elaborate fantasy about O'Brien's involvement in an underground movement. This is sheer wish fulfillment on Winston's part. Ironically, O'Brien is not only not part of a resistance, he is working to trap Winston so that he can later torture him into becoming a proper Party member.

This reference occurs in Part II, Chapter 6, and comes in the first conversation that Winston Smith and O'Brien have. The importance of this conversation is shown through the way that Winston Smith believes this is the rebel group against Big Brother making contact with him, and this is cemented when O'Brien deliberately makes a reference to Syme, who has recently disappeared. This reference is a crime, because Syme, as the narrator tells us, is not an "unperson." Note what Winston Smith thinks about this reference to Syme:

O'Brien's remark must obviously have been intended as a signal, a code-word. By sharing a small act of thoughtcrime he had turned the two of them into accomplices.

This is shown to be ironic later on in the novel, because it turns out that O'Brien is not guilty of thoughtcrime: he is a high-ranking member of the Party whose job it is to locate and find members of the Party, such as Winston Smith, who are opposed to Big Brother and then "recondition" them so that that hatred is replaced by love. The irony of this text is based on the way in which Winston interprets this remark as being a symbol of collaboration against Big Brother, whereas the reality is completely the opposite.