I won't write a whole paragraph but i'll list the symbolism. The gold represents the purity and value they had at the time, the hair of the wife represents the youth the woman once had, and the chain represented the emotional attachment she had for her husband.
In "The Gift of the Magi," the symbols that are present are linked with the Bible, making the story a kind of parable. First of all, we have the gifts that the two characters exchange. Della decides to sell her hair, while Jim sells his watch. Della's hair is compared to that of the Queen of Sheba, while Jim's watch is said to be the envy of King Solomon.
By comparing these items with Biblical, royal figures, the author wants us to realize the enormous value that the items have for the couple. He also wants us to understand that the two lovers are really as rich as the Queen and King, because they have the most valuable thing on Earth: love. This is also why the lovers are compared to the "Magi," or the three wise men, at the end of the story.
