What is the significance of the refrain by the women whose house was burned? What did it mean? What was its effect on Montag?

This is such a powerful moment in the story. Montag and some of his fellow firemen break down the door to a woman's house. The woman says, "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." Beatty later explains this to Montag. In 1655 a man named Latimer said this to his fellow Nicholas Ridley before they were burnt alive for heresy. Heresy was when the church interpreted pretty much anything they wanted, usually ideas not in line with strict church doctrine, as crimes against God. The connections are striking. Just like the two men were ready to burn for their beliefs, the woman is ready to burn for her books. She wants to be a living burning beacon to the travesty of destroying knowledge. This makes a profound impact on Montag. He "liberates" (steals) a few books and lays awake all night pondering the powerful horrific message that he has beheld. I hope this helps you!

IT WAS OCTOBER 16, 1555. NOT 1655.