What is the significance of the ending of No Country for Old Men?
The ending of No Country for Old Men has elements that are clear-cut, and elements that are ambiguous.
Chigurh kills Carla Jean after delivering a short monologue that explains his perceptions;
You can say that things could have turned out differently. That they could have been some other way. But what does that mean? They are not some other way. They are this way.
Chigurh functions both as a visceral character and as a personification of force. Interpretations vary, but he definitely embodies values and themes such as fate and death. His words, as quoted above, can be applied both to Carla Jean's position as well as society as a whole. A persistent theme in NCFOM is the presence of evil and how people react to it; if Chigurh does function as an embodiment of evil, then his words are meant to establish the permanence of evil.
The actual "ending" of the story is a series of narrations by Tom Bell following his decision to retire; he struggles to come to terms with his inability to confront and defeat evil, as personified in Chigurh. His final narration concerns a series of dreams about his father;
I dont remember the first one all that well but it was about meetin him in town somewheres and he give me some money and I think I lost it. But the second one it was like we was both back in older times and I was on horseback goin through the mountains of a night. Goin through this pass in the mountains. It was cold and there was snow on the ground and he rode past me and kept on goin. Never said nothin. He just rode on past and he had this blanket wrapped around him and he had his head down and when he rode past I seen he was carryin fire in a horn the way people used to do and I could see the horn from the light inside of it. About the color of the moon. And in the dream I knew that he was goin on ahead and that he was fixin to make afire somewhere out there in all that dark and all that cold and I knew that whenever I got there he would be there. And then I woke up.
It is interesting that Bell brushes past the first one, as though it is relatively insignificant. One way of interpreting it is that Bell feels irresponsible and incapable of living up to his father's expectations, and the lost money represents a loss of valuable things, such as Bell's honor or the meaning of his role as a sheriff.
The second dream contains richer material to interpret. What does seem clear about it is that Bell's father represents a powerful figure, one whom Bell is impressed by and looks up to, that the snow and cold represent some sort of oppressive force, and the fire in the horn represents something of value. One means of interpreting this is that, by being set in the "olden days", Bell's dream implies that the old way of doing things, i.e. a simple fire to keep away the cold, is gone and will never return. Another significant point is that he wakes up before he reaches the fire; this may signify that Bell is eternally lost.