The denouement, or resolution, of "The Gift of the Magi" is that while Jim and Della do not have what they need to make use of their Christmas gifts, these gifts are anything but worthless. For, they are proof of the real gift that each has given the other: His and her love. Della is willing to sacrifice her luxurious hair--hair that would "depreciate the Queen of Sheba's jewels" in its beauty. She makes this sacrifice in order to buy for her darling Jim a watch chain which she feels his gold watch deserves. Likewise, Jim generously sells his gold watch--which even Solomon would envy--to buy decorative combs to adorn his wife's lovely hair.
As O. Henry tells the reader, these "foolish children in a flat ...most unwisely sacrificed for each other the greatest treasures of their house. But, he continues, "...such as they are wisest. Everywhere they are wisest. They are the Magi."
"The Gift of the Magi" is a lovely story for Christmastime. It teaches the reader the meaning of giving: Love. And, it is this selfless love that makes Della and Jim "the wisest." This is the denouement.
The denouement means the unraveling of the plot--the final "tying up" of the loose ends. In "The Gift of the Magi," O. Henry creates tension by having Della and Jim each give up what is most precious to them (and to each other) in order to buy gifts for each other. And, of course,the irony is that they cannot use the gifts now. We wonder if they will be angry or disappointed. However, the denouement--again, tying up those loose ends--lets us see that they both realize how loving the other's actions were. Della says that they'll put away the combs and the watch fob for now. Her hair will grow back and they may be able to buy back the pawned watch. For now (in a most satisfying denouement) they are simply happy to have each other and their love.