Ending spoilers abound.
"And then I woke up.."
Llewelyn Moss, ostensibly the protagonist of the movie, is dead. He died offscreen. The mysterious implacable man who had been chasing him, leaving a path of destruction in his wake, is gone. Now the movie decides to tell you what it's actually been about all this time.
Ed Tom Bell, the sheriff who has - through no fault of his own - always been one step behind the action, is left to sort out what it all means, if anything. If nothing else, most of the folks in the audience wanted some sort of neat summary or something. Instead, a broken sheriff discusses with his wife a couple of dreams he'd had.
"Alright then. Two of 'em. Both had my father in 'em . It's peculiar. I'm older now then he ever was by twenty years. So in a sense he's the younger man. Anyway, first one I don't remember too well but it was about meeting him in town somewhere, he's gonna give me some money. I think I lost it. 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' goin' by. He just rode on past... and he had his blanket wrapped around him and 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. 'Bout the color of the moon. And in the dream I knew that he was goin' on ahead and he was fixin' to make a fire 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..."
...and then the credits roll.
Lots of people seem to hate this ending. I love it. Rather than go on and on about the deeper meaning behind it, I'll just mention that it's a damned good way to end a movie, just on a cinematic level. Tommy Lee Jones is spot perfect (I know Javier Bardem won the Oscar for best supporting actor, but it feels like it could've gone to Jones just as easily).