You can find that information right here on eNotes! I have included a link and also included my own summary here for you.
The narrator of the story admits that, upon waking, anyone in the house can hear a "door shutting." Both the narrator and her husband live in a home that has many memories trapped within its walls. The narrator remains unafraid even though there are numerous accounts of doors and windows opening and closing. As the two ghosts wander through their home, both husband and wife know these ghosts mean the couple no harm. Instead of wreaking havoc, the ghosts are simply searching for something. The focus of their search seems to center upon the garden or the loft. This intrigues the narrator, who is incredibly interested to see what the object could possibly be: an object that two ghosts are searching for.
It isn't long before the house itself responds to the desperate search of the two ghosts. The pulse of the house races as the two ghosts are about to discover the object of their search. The narrator is lucky enough to hear the house's "heartbeat" as the word "safe" is repeated again and again and again. The house reveals other things to the narrator as well. There is a great treasure hidden within the rooms of the house: perhaps the goal of the two ghosts.
Somehow, the narrator learns about the lives of the two ghosts. They were man and wife as well (hundreds of years ago). After the woman dies in tragedy, the man abandons the house only to wander the earth. Only after his death did he return to reunite with his deceased wife. Through this information and through the conquest of the search itself, the narrator finds the intent of the ghosts' search. They seek a loving relationship and the happiness it brings.
The ghosts find a kind of kinship in the narrator and her husband because they share the same type of joy in their loving relationship. Suddenly, the narrator awakes to the ghosts' silver lantern and knows that her relationship is what the ghosts were looking for. Their treasure is buried within the love of the narrator and her husband.