The diamond Moonstone itself is an emblem of the past – it has been an important religious icon for centuries before Colonel Herncastle stole it. It stands to reason, then, that the novel named after the Moonstone should be interested in the ways that the past comes back to haunt the present. Most of the novel is being narrated by characters who are looking back on the events of a year or more before, so there's a lot of discussion of how, exactly, they're recalling these past events in such detail. Some of them have journals or diaries that they can look back on, others are relying on memory alone. Which are the more reliable narrators?
The Moonstone itself can be seen as an emblem of the past and the ways that history continually disrupts the present.
Only by repeating the past, through the experimental reenactment of the night the Moonstone was lost, can Franklin and Rachel understand it, come to terms with it, and move forward.