The father tells his son he must go on in order to "carry the fire." He says: "It's inside you. It was always there." [p. 279]. What is this fire?
His father is referring to the human spirit, the will to survive that has kept them going from the moment of the disaster, through the suicide of his wife and the son's mother, and through every horror and tragedy they have experienced on the long road to the coast.
In essence, this is why the book, even though it seems thoroughly depressing most of the time, is actually a story of hope and survival. Humans will do almost anything to survive, and these two characters have, obviously, at great personal expense to their psyches and their physical well being. The struggle takes the father's life, and in this quote, he is telling the son to survive and carry on.
The fire to which the father refers is the undying flame which exists in all of us. This "fire" is the fire of suffering and of existence and of hope. It is the flickering essence of humanity.
The very fact that the father states "it was always there" shows this flame of humanity which burns within the son as a natural element, a ready connection to any other possible human being or "good guy" which may exist in the world, and which eventually does show up in the plot. A small fire can only grow if it is fed with life, oxygen, spirit.
The father knows that if the son can continue on the journey, if he can continue to survive, since he is one of the "good guys" then humanity has a shot to survive even in this desolate world.