The woman was strongly affected by the presence of the firemen. It says,
"She was only standing, weaving from side to side, her eyes fixed upon a nothingness in the wall, as if they had struck her a terrible blow upon the head." (pg 36)
She then quotes Hugh Latimer who was put to death for heresy by burning at the stake. Heresy is not agreeing with the governments' or power in authority's stance on something. The woman, obviously, did not believe in the government's stance on book burning. She had made her decision at that time. She had in her hand a match. She died by her own hand and chose to burn with her books.
This had a profound affect on Montag. He tried to save the woman. This was the first time he had seen a human victim. Before this,
"You weren't hurting anyone, you were only hurting things! And since things really couldn't be hurt, and things don't scream or whimper, as this woman might begin to scream and cry out, there was nothing to tease your conscience later." (pg 36-37)
But this was his first victim. He felt that the police should have removed her first before they started burning the books. He pleaded with Beatty to remove her. Beatty just conceded that she was going to commit suicide and that was the way it was.
"She made the empty rooms roar with accusation and shake down a fine dust of guilt that was sucked in their nostrils as they plunged about." (pg 37)
Montag went home after that shift and felt deep sorrow. He felt sick. The smell of kerosene made him vomit. When he tried to talk to Mildred about it, he found his wife unfeeling. He tried to talk with her and says,
"There must be something in books, things we can't imagine, to make a woman stay in a burning house; there must be something there. You don't stay for nothing." (pg 51)
This was the beginning of his rebellion. It jelled his desire to read books with his passion to learn from them. It was the impetus to move him forward and search out Faber.
The page numbers I have given you are from my version of the book, but they should be in close proximity.