Montag and Mildred are married, and are not happy but function together as a unit. Mildred's existence is centred around the television, a screen that takes up an entire wall. Her desire is to have television screens in all four walls. This would completely box her in. It would symbolize her total separation from the world outside of the television. Mildred's television characters are more real to her than her relationships in real time. However, she is unhappy. Montag comes home to find that she has tried to kill herself. It is as if the television has created her alienation but she has no way to articulate the pain she feels. In fact, she is so numb, she herself seems to be only remotely aware of it.
Montag, on the other hand, faces a breakdown of the walls that keep him within the bounds of his society. When he starts to read, he starts to question the value of book burning.
The wall between the two of them is most apparent here, when Montag tries to share his thoughts with his wife. She feels threatened and afraid and closes herself off from him completely.
The physical walls in their house, and the television screens that fill them represent the isolation,emptiness and alienation of the society. There is no real intimacy between Mildred and Montag, because all of Mildred's love and care goes to the imaginary characters on television, all of whom are more "real" to her than people or characters in books. The only chance for intimacy in this relationship is the absence of the fourth wall. When that is filled, no hope remains.
In theatre, the fourth wall refers to the imaginary wall between the actors and the audience. The actors are supposed to maintain the illusion that the fourth wall exists, and to act as if they are on a contained set. Breaking the fourth wall occurs when the actors speak directly to the audience. To do this is to acknowledge that they are aware that they actors acting a role.
Mildred wanting the fourth wall suggests that she wants to be contained in the world of the actors, and does not want to interact with the "audience"--in this case, her husband and other people in her society that do not share her involvement with her fantasy world.
What Mildred doesn't know, and what Montag slowly discovers, is that their entire society is built on a carefully constructed fantasy in which all potentially threatening ideas are banished (burned) before they can infect society.