Both of the Tyrone parents have a carefully hidden object that they used to look at every once in a while to remind themselves about what they've lost. Mary's wedding dress brings to mind her happiness with her father, innocence, youth, beauty – what you will. James keeps a piece of paper printed with praise from famous actor Edwin Booth of James's performance of Othello.
The dress and the paper each stand in for a history that's dead to the Tyrones, leading to the loss of the objects themselves. The wedding dress, however, is recovered in the final scene, as Mary regresses back to childhood – crazily and artificially, but still, she does seem to recover her lost history, for a time.