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.