The most significant and main use of irony which is focused on in this story is the situational irony that occurs at the end of the tale. Situational irony is when we expect a certain thing to happen only to be surprised when something entirely different takes place. We can see the situational irony in operation therefore when we realise that both Jim and Della have sold what was most precious to them--their hair and watch--to buy a present for the other to use with what was most precious to them.
However, a deeper irony exists in the story. Although we are tempted to dismiss Jim and Della and their actions as "foolish," yet the narrator insists that they were in fact actually "wise" because through their self-sacrifice and love they represent the original spirit of the Magi:
But in a last word to the wise of these days, let it be said that of all who give gifts, these two were the wisest. Of all who give and receive gifts, such as they are the wisest. Everywhere they are wisest. They are the Magi.
Thus Jim and Della, although apparently "foolish" in the eyes of the world, ironically come closest to the original spirit of present giving.
Another example of situational irony in the story is the name on the mailbox. When one hears a name such as "Mr. James Dillingham Young," one would likely be inclined to believe that this person would be of high status—going by all three names sounds a little pretentious. Further, there's something about the name "Dillingham" that sounds rather upper crust. However, the James Dillingham Youngs are actually not of a high status at all; in fact, they lack status and even enough money to purchase each other one Christmas gift (before selling their most prized items).
A further example of situational irony is that, despite the fact that the narrator says that if a king lived with the Youngs in their apartment, Jim "would have looked at his watch every time they met," the narrator later says that "he sometimes took it out and looked at it only when no one could see him do it" because the watch never had a fine chain to go with it. Despite the watch's value in terms of money as well as sentiment, Jim is embarrassed to take it out in public. Such irony underwrites Della's desire to purchase a beautiful chain for Jim's watch.