The resolution to "The Gift of the Magi" occurs when Jim tells his wife they should "put our Christmas gifts away and keep them a while. They’re too nice to use now." He says this because he, like his wife, sold his most prized possession—he his watch, she her hair. Both bought something for the other's prized possession; Jim bought Della combs for her hair and Della bought Jim a chain for his watch.
The story resolves in this way in order for the narrator to explain that these "children," as the narrator calls them, are "not wise" for selling what matters most to them, but are "the most wise" because "Each sold the most valuable thing he owned in order to buy a gift for the other."
The story resolves simply and demonstrates the love the young married couple has for one another. Instead of resolving in tragedy, like Della crying like she does in the beginning of the story, or frustration, Jim suggests, with a smile on his face, the two should sit down and have their dinner.
This a great question. The resolution of the short story, "Gift of the Magi," is when both main characters learn that the greatest gift is to give what they possess to one another in view of love. It is the paradox of getting when giving. Let me explain.
In the story, the two main characters sell their most prized possessions to give to each other something for Christmas. Della cuts and sells her hair to buy Jim, her husband, a chain for his watch. Jim sells his watch to buy Della combs for her hair. In light of this, they both seek to outdo one another in love.
As you can tell, in the end both have gifts that they cannot use. Della does not need combs and Jim no longer needs a chain for his watch. However, O. Henry calls them wise, because they love sacrificially.