The resolution of the short story is when all is revealed and both Jim and Della sit down to eat dinner.
In the beginning of the story, Della is feeling down, because it is Christmas and she does not have enough money to buy Jim something. So, she sells her beautiful hair, her most prized possession, to buy Jim a chain for his watch. Jim, on the other hand, sells his watch to buy costly combs for Della's hair.
When Jim comes home, he see Della's hair cropped short. She finally has the combs that she wanted, but she cannot use it. In any case, Della is moved. Now its her turn to present her gift. A gold chain. Jim tells her that he sold the watch to get the combs. This is when they both see the extent of love. Here are the words of O. Henry:
Jim...
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sat down and smiled.
“Della,” said he, “let’s put our Christmas gifts away and keep them a while. They’re too nice to use now. I sold the watch to get the money to buy the combs. And now I think we should have our dinner.”
Both know the thoughts of the other. They both experience love. Both are moved. That is enough. So, they eat together.
At this point, the O. Henry breaks in. They are wise, because they know the value of giving.
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.