In part 3 of "Fahrenheit 451", what does the campfire in the forest represent?
In this novel, fire, for the most part, represents destruction. In the society of the story, the firemen don't put out fires, they start fires in order to destroy books. We see a woman who loved her books so much, she let fire destroy herself rather than live without her books. Montag's house is destroyed by fire and Capt. Beatty himself is destroyed by fire. When Montag emerges from the river and walks toward the woods, he sees the fire in the distance like a "winking eye", i.e., he sees it then it disappears and then he sees it again. Montag notes that this fire was different from the fires of his former society, this fire was was warming. This time, the fire didn't destroy; it created. It created warmth for people to gather around. Fire now means something good rather than something bad. This represents the new society that Montag and the other book people will try to create. They want a society that is the opposite of the former society.
It represents a new hope, a new start. Just as the people living there have "returned" to the past, so the campfire is a "return" to times when technology did not complicate the process.
It is also showing fire being used properly: as something for our good, our benefit (not for destruction, but for life-giving warmth). The connection can then be made to the books in the minds of the people there--they are also being used properly, edifying, giving life.