The phrase "carrying the fire" comes up four times in Cormac McCarthy's The Road and is said eight times in those four scenes. It also appears as "carry the fire" in the scene where the man dies. Carrying the fire signifies hope for the human race; though the world seems all but over, as long as someone is alive and trying to thrive, they're still carrying the fire, which means the human race still has hope.
When the boy is scared early in the novel, his father assures him that they will be okay. When his father agrees nothing bad will happen, the boy says, "because we're carrying the fire." His father affirms this, saying "Yes. Because we're carrying the fire."
The next time the phrase appears, it's after an encounter with cannibals. The man promises the boy that they won't ever eat anyone. He says they're the good guys and that they're carrying the fire. That light for humanity means that they can't turn their back on being the kind of people who don't exploit others and eat them for food.
The third time the boy says the phrase, he's asking his father about the possibility of finding another father and son like them. He says, "And they could be carrying the fire too?" The man assures him that it's possible but that they can't be sure. He's trying to teach his son to be wary without extinguishing the hope that there are still good people in the world.
When his father dies, he insists that the boy has to go. He charges his son with carrying the fire. He tells him:
You have to carry the fire.
I dont know how to.
Yes you do.
Is it real? The fire?
Yes it is.
Where is it? I dont know where it is.
Yes you do. It's inside you. It was always there. I can see it.
In this way, his father shows that the fire isn't a real fire. Rather, it's the drive that keeps humanity going and the hope for a better world.
The boy accepts what his father says and goes with the man at the end of the novel. He asks the man whether he's carrying the fire—the fourth and final time the complete phrase appears—and the man doesn't understand what he means but finally says that, yes, he's carrying the fire.
The boy goes with the man.