What does the old lady on North Elm Street do that surprises the firemen?
The short answer to this is that she sets herself and her whole house on fire.
The woman you are talking about has a whole bunch of books in her house. One of her neighbors has betrayed her -- has turned her in to the authorities. So Montag and his fellow firemen have come to burn her books and her house.
They tell her to get out, but she takes a match and strikes it against the porch railing. The whole house goes up because the firemen have sprayed the kerosene.
This act is one of the things that really gets Montag to start thinking about rebelling.