In this part of the novel Montag and other "firemen" go to a woman's house and "crashed the front door." The woman said, "Play the man, Master Ridley; we shall this day light such a candle, by God's grace, in England, as I trust shall never be put out." This was later explained to Montag by Beatty, " A man named Latimer said that to a man named Nicholas Ridley, as they were being burnt alive at Oxford, for heresy, on October 16, 1555."
This is significant because the woman is indicating that by burning the books and her burning with them will make people begin to see how wrong these actions are. She is hoping her sacrifice will lead to long term change.
"The incident with the unnamed woman only aggravates Montag's doubt and alienation. This event helps raise Montag's consciousness about his work. He is so upset that he lays awake all night, so upset that by morning he feels too sick to go to work." He was also so moved that he actually took some of the books and hid them in his jacket and took them home.
In Fahrenheit 451, the refrain repeated by the woman is an allusion to Hugh Latimer, a Christian martyr who was burned at the stake for heresy in 1555. By repeating his final words, the woman is making a comparison between Latimer and herself: like him, she is about to be burned for possessing illegal books, something which she deeply believes in.
We see Montag's reaction from the text. First, he pleads with the woman to leave the house before it is set alight and, when she refuses, he repeats her refrain to Beatty and asks what it means. The full extent of his reaction becomes clear later, however, when he is at home with Mildred. He asks her about the first time they met and how many sleeping pills she has taken. He is angered by her emptiness and her love of the parlor walls. In sum, he is beginning to completely re-evaluate his society, his life and its purpose.