In the final paragraph of "The Gift of the Magi," O. Henry refers to the original magi, the three wise men who "invented the art of giving Christmas presents." He contrasts the wisdom of these gift-givers with the folly of Jim and Della, "who most unwisely sacrificed for each other the greatest treasures of their house."

So far, the contrast between ancient wisdom and modern folly is straightforward, but O. Henry then complicates it. Jim and Della have been impractical in the gifts they chose and the sacrifices they made, but their folly contains a wisdom higher than prudence. Their love for one another, and their understanding that this is all that really matters, make them the magi, the wisest people of all.

The true significance of the story's title emerges in this point, and is highlighted by what appears to be a small detail. The title is not "The Gifts of the Magi" but "The Gift of the Magi." It refers, therefore, neither to the gold, frankincense and myrrh brought to the infant Jesus by the three wise men, nor to the combs and the watch-chain Jim and Della bought for one another. The gift which Jesus gave to the magi, and to the world, was love. It is this gift that Jim and Della give to one another, and without which any other gifts are meaningless.

The title of O. Henry’s story alludes to the popular story of the three “magi” or wise men who visited Baby Jesus soon after his birth. The wise men came bearing gifts of gold, myrrh, and frankincense, and this story is also about the giving of gifts. Della gives Jim a new watch fob and Jim buys Della lovely combs for her hair. The fact that the story is set on Christmas Eve adds to the significance of the allusion to the three wise men.

Jim and Della’s real gift to each other, however, is the indication of the depth of their love for one another, since Della sold her hair for money for the watch fob, and Jim sold his watch for money for the combs. While their gifts are therefore rendered useless, each is left with a powerful indication of the depth of their love for one another. It is this love for each other that makes O. Henry declare them “the wisest” of all gift-givers.

The significance that O. Henry places in his title of “The Gift of the Magi” refers to the wisdom that Jim and Della have gained in realizing that the love they share is more valuable than any physical gift they could give to one another. Each gift brought by the magi had a deeper meaning. Gold is a symbol of royalty, while frankincense represented deit,y and myrrh symbolized death or suffering. In the same way, Jim and Della’s gifts showcased the deeper meaning of their love for one another.

The title does allude to the three wise men from the Bible, kings that come from far away to bring the Christ child gold, frankincense, and myrrh: expensive and precious gifts to honor him. However, at the end of the story, the narrator says of Jim and Della, "Of all who give and receive gifts, such as they are the most wise. Everywhere they are the wise ones. They are the magi." Therefore, the title of the story doesn't simply allude to the original magi; the title actually refers to Jim and Della Young because they are the magi.

The narrator calls them the "most wise" because they understand that nothing in the world is as valuable as love. They both sacrifice the thing they own that is most important to them to show their love for the other: Jim sells his beautiful watch to buy Della hair combs, and Della sells her hair to buy Jim a watch chain. Their gifts require sacrifice, and the gifts given by the three rich kings did not: that makes Jim and Della the real magi.

The title of the story refers to the three "wise men" or magi who are supposed to have come bringing precious gifts to present to Jesus at his birth.

O. Henry used this title because of the idea of precious gifts and the idea of wisdom that the title alludes to.  Jim and Della are trying to give each other what they think are the most precious gifts they can possibly come up with.  Unwittingly, they give each other an even more precious gift -- the proof of the depth of their love for one another.  As O Henry says at the end of the story, their gifts, and their reaction to those gifts, shows that they are truly wise.

So -- the title alludes to a story of wisdom and precious gifts.  O Henry's story is about these same things.