1984 is a novel about a grim future in which society is controlled by Big Brother and the Party. One of the Party's chief functions is to eliminate emotional attachments between people, replacing the need for human companionship with devotion to the Party and its goals.
At one point in the story a girl passes a note to the main character Winston Smith. An ironic situation ensues in which Smith, who is flabbergasted by this unexpected event, tries to process the fact that this person, who he had previously thought of as an enemy, has made such a dangerous overture toward him.
The irony lies in the fact that the event throws Winston into such a quandary. Normally, such an instance might be likely to make the recipient happy or curious or expectant. But in the reality of 1984, it is a cause for worry and caution. Winston goes to great pains to find a safe place and time to first read the note and then to think about it. The Party has done such a good job of keeping its citizens occupied and inebriated that it is almost impossible to find a way to think and consider.
It was not till twenty-three hours, when he was home and in bed--in the darkness, where you were safe even from the telescreen so long as you kept silent--that he was able to think continuously.
Winston and Julia eventually do get together, and their relationship infuses some meaning into their lives. Unfortunately, however, the Party is much too powerful and their relationship is eventually discovered. This leads to the devastating interrogation and torture that they both must experience.
What is ironic about this particular section of the novel is the way that when Winston sees Julia striding towards him as they are together in this corridor, he sees her as a figure representing danger as well as also a figure who has just fallen and hurt herself. Note how this is described:
A curious emotion stirred in Winston's heart. In front of him was an enemy who was trying to kill him: in front of him, also, was a human creature, in pain and perhaps with a broken bone.
The irony is based around the way in which Julia is at one level the character who will be responsible for Winston's downfall, as it is through pursuing their relationship together that he is caught. Therefore, Julia is his enemy in more ways that Winston is aware of. Also, it is ironic because he assumes Julia is a supporter of Big Brother and therefore his enemy, when in fact she is just as opposed to Big Brother as he is.