In the story, "The Gift of the Magi," the characters of Jim and Dehlia, the husband and wife in the story are representative of the Magi, described in the other two answers. O Henry uses this title particularly to highlight the uniquely sacrificial love that Jim and his wife share.
It is a rare occasion for self-sacrifice to dominate a relationship in the way the it does Jim and Dehlia's marriage. Their personal sacrifices made for each other, symbolize for O Henry the great love and respect that the Magi showed the infant Jesus. Like the Magi, who traveled far and with great risk to personal safety, Jim and his wife surrender their most valued personal possessions to buy gifts for the other.
The other is more important than the self in this story, that is at the heart of the theme, love, sacrifice, and an understanding of a greater gift that has nothing to do with material possessions.