What would "keep the home fires burning" mean in this society?
In Fahrenheit 451, the firemen do not fight fires, but start them. They are responsible for tracking down homes that still contain books, which have are illegal. When a house has books, the firemen burn the house to the ground. Keeping this in mind, the phrase, "Keep the home fires burning," is like a good luck salute or a mantra for the firemen. The more fires, the more illegal books are being burned, the more the people who are keeping books are being punished, and the better the firemen are doing their jobs.