The "Ring" is an old Roman amphitheater (like a smaller version of the Colosseum in Rome) just outside Casterbridge. The narrator tells us something about the history of the place: during Roman times, it was used for public entertainment. In later years, it was used for public executions. More recently, it had been used as a place to meet for private duels. The circular seating screens the interior from the road, so no one passing by can see what's going on inside.
The Ring is an important setting in the novel for two important scenes: Henchard's first reunion with Susan and his meeting with Lucetta. During the second, the narrator even remarks on the similarity between the two scenes. The Ring's ancient history and the fact that scenes tend to repeat themselves there suggest that the Ring might be an emblem for the way the past comes back to haunt the present. Characters cannot escape their history.