The "fire" in this text is a very important symbol of both hope and humanity. McCarthy presents the reader with a grim and relentless dystopian world which offers little hope or future for humanity. The remnants of the human species are forced into cannibalising each other merely to survive or scavenging for tins and other dried goods thanks to some kind of unspecified disaster that has overtaken the planet. As a result, the humans in the book are presented as shadows of their former selves, debased and animalistic in the way that they prey on each other and have lost any sense of moral code. It is only the father and the son in this text that offer some kind of hope for humanity, and it is this that is captured in the phrase "carrying the fire." Note how this is directly addressed when the father realises he is dying in the injunction he gives to his son:
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 the father's description of the fire, it is clear that the way he talks about the fire being "inside" his son, and "always" being there, is something that points towards its symbolic meaning. The fire that the boy is told to continue carrying represents the hope for humanity. This is why when the boy meets the man who will take care of him he instinctively asks whether he carries the fire. As long as this symbolic "fire" burns, there is still hope for the future of humanity in this grim world.