The One is the name of the oldest of The Undying, who are gods or tutelary hearth spirits who are worshipped or revered by the people of the Riverlands. The family of Closti the Clam has a very old hearth statue of some kind of dark metal with sparkling flecks in it. Each spring after the floodwaters go down, the statue is put into a fire for renewal. There is a ritual about it. The fire is a large one, carefully made, and the statue stands on a ledge in the middle of it. The statue is not ready to come out until the fire has subsided completely into ashes. When he emerges from the fire, he is at his strongest.
The family has two other statues, but they are not metallic, and do not have the same fire ritual. It is generally believed, though, that the three are related in some fashion. One is The Young One, and the other is The Lady. All three of the Undying play a role at one point or another in the novel.