Symbolism, Imagery, Allegory
Stories. Everyone loves 'em. That's why Odysseus tells and listens to them all over the place, and it's why Americans spend billions every year at the theater.
In this book, they symbolize all sorts of things. For one thing, they're a measure of trust between two people, as Frazier explores when Inman is willing to tell his stories to the goat woman:
He looked her in the eyes and was surprised to find that they were wells of kindness despite all her hard talk. Not a soul he had met in some time drew him out as this goatwoman did, and so he told her what was in his heart. (11.125)
Inman isn't willing to tell all of his story to everyone he meets along the way, so when he starts telling his stories to this old woman, it shows that he has faith in her kindness.
Stories are also a way of explaining things that happen in the world and the way a character perceives the world's nature, as when Ada and Ruby explore their understandings of life by telling stories to each other. They're even a way of charting a course in life, since time and again the characters think of stories as a way of imagining their lives. When someone tells a story in Cold Mountain, it's probably there for a reason.