In Fahrenheit 451, when Montag explains to Faber that "my wife's dying," what does he mean?
I assume that you are talking about the part where Montag first goes (on the subway) to talk to Faber. He wants Faber to be his teacher. Faber says that Montag is brave and Montag replies by saying that he's not brave but that his wife is dying, a friend has died, and another person who could have been a friend died as well. When Montag says that Millie is dying, he does not mean it literally. Instead, he is speaking about Millie's soul, her humanity.
Montag is trying to explain why he stole the book. He is trying to tell Faber that he did so because he was driven to it by how desolate their society is. That's why he says Millie is dying. She is dying inside because their society does not want people to think or to have normal human feelings for one another. The ban on books is a part of this.
So Montag is explaining why he stole the book. He is saying that their society either kills people literally (Clarisse, the old woman) or kills their humanity (what has happened to Millie). Because their society does this, he feels he must fight back and that is why he has stolen the book and come to Faber.
As was mentioned in the previous post, Montag makes this figurative comment during a conversation with Faber. Montag initially visits Faber in order to receive help comprehending various texts. During their conversation, Montag tells Faber that his wife is dying and he's already lost one of his friends. Montag does not mean that his wife is literally dying, but implies that she is spiritually dead. Mildred is obsessed with her parlor walls, addicted to sleeping pills, and lives a meaningless life. She refuses to accept the fact that she lives an unhealthy lifestyle, and has even overdosed on sleeping pills. Montag recognizes that Mildred is living a reckless, unfulfilled life. He believes that she is both spiritually dead, and is aware that her current behavior could result in suicide.