The irony found in the short story "The Gift of the Magi" is called situational irony, since the outcome is not what is expected, as further explained below.
In literature, we call situational irony those events in a story where the outcome or consequence is not what we expected. That is the type of irony we have in the short story "The Gift of the Magi."
The characters Della and Jim are wife and husband. They love each other very much and, because they lack money to buy each other gifts for Christmas, they each sell their most valuable possession. Jim sells his watch and Della sells her hair.
It turns out that Jim buys Della beautiful combs for her long hair, and Della buys Jim a fancy chain for his watch. In the end, one cannot wear the gift bought by the other. This is where the situational irony lies. No one, not even the readers, expected such a thing to happen.
Learn more about situational irony here:
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