In O. Henry’s short story, “The Gift of the Magi,” Della buys her husband, Jim, a “platinum fob chain” to go with his pocket watch.
In this story, we are told that Jim Young (James Dillingham Young) has one possession of which he is very proud. This possession
was Jim's gold watch that had been his father's and his grandfather's.
In the days when this story is set, people did not wear wrist watches. Instead, men had pocket watches that they carried in their pockets. The fob chain attached to the watch and was secured in a different pocket than the one in which the watch was carried (please read the annotations in the link below to see an excellent discussion of the importance of fob chains for men who owned pocket watches). The fob chain would ensure that the watch would not fall on the ground and break if the owner accidentally dropped it.
Della buys the platinum fob chain for Jim because it is something that he would love to have. She sacrifices her own prized possession (her hair) in order to do so. In doing this, she is demonstrating how much she loves her husband.