This section of the novel comes in the first part, "The Hearth and the Salamander" and comes at a crucial time in the novel straight after Montag has witnessed a woman's act of suicide rather than facing life without her books. This of course taps into Montag's own awakening sense of emptiness and lack of sense of purpose, and when he gets back to his house he finds himself looking at his wife and questioning their relationship:
And suddenly she was so strange he couldn't believe he knew her st all. He wa sin someone else's house, like those other jokes people told of the gentleman, drunk, coming home late at night, unlocking the wrong door, entering a wrong room, and bedding with a stranger and getting up early and going to work and neither of them the wiser.
This quote and the part you are referring to comes on page 42-43 in my edition of the novel, but the important thing to focus on is how this highlights the growing impression of dislocation in this dystopian society. Dislocation not just from history and literature, but also within relationships - the society encourages and facilitates superficial relationships with no meaning, and no value. This is what Montag is realising as he contemplates his own emptiness.
On page 40 of Simon & Schuster's 60th Anniversary Edition of Fahrenheit 451, Mildred tells Montag that she doesn't remember where or when they met. Montag had recently begun to examine his life after his conversations with Clarisse and realized that he wasn't happy. Montag then witnessed a woman commit suicide because she refused to leave her books. When Montag returned home, he asked Mildred a simple question regarding when and where they met in order to confirm his feelings. Mildred told Montag that she forgot and casually dismissed the significant question. Mildred is the typical, superficial citizen in Bradbury's dystopian society. She is self-centered, callous, and shallow. Mildred only cares about her parlor televisions and is addicted to sleeping pills. She is unaware of her husband's feelings and never takes time out of her day to listen to him. Mildred is constantly listening to her Seashell radios which leaves no time to develop a loving relationship with Montag.