The woman refuses to leave her books and chooses to die with them because she understands the value of literature. She cannot imagine life without reading or intellectual pursuit in Bradbury's dystopian society and would rather die than live a life without literature. The woman is also taking a stand against the authoritarian regime by refusing to capitulate to their demands. Witnessing the woman commit suicide and die with her books has a profound effect on Montag. Montag realizes that there must be something of value in the books that would cause the woman to lay down her life for them. He begins to feel ashamed and guilty for destroying books and attempts to discover the valuable contents in various novels. Montag sees the passion that the woman had for her books and understands that literature may provide the vital answers necessary to give his life meaning.
The unnamed woman refuses to leave her books because they are vital to her. In this shallow society of the future, they are all that are valuable to her. She is also making a statement by igniting the flames herself - that she would rather die than lose what she believes in.
This is a pivotal moment for Montag. For it causes him to question what the firemen are doing. If a person could so love books and find them so important as to burn alive with them, then what is the power and mystery of books and the words they contain? It is no wonder then that Montag stashes away one of the lady's books.
During the night he cannot sleep. He keeps thinking about her and searching for meaning in his life. One might wonder if Montag isn't questioning himself on whether he has anything so meaningful in his life that he would die for it.