The magi didn't, technically, invent anything. They were wise men or magicians and probably astrologers. Because astrologers watched the skies and could predict where the stars and planets would move to, they were considered to be able to foretell the future.

The magi in the Bible foretell that the Messiah has been born and determine where he is. They come to visit him and bring him gifts to honor him. They are able to look past his humble surroundings and see the divinity that surrounds him.

What they "invented"—what has followed from their example—is the tradition of gift-gifting to celebrate the birth of Jesus. This gift-giving, ideally, is understood as an outpouring of love and reverence in response to God's gift of giving Jesus to the world.

In "The Gift of the Magi," O. Henry compares the loving, sacrificial gifts of Jim and Della to the gifts the original magi gave Jesus.

The magi, or the Three Wise Men, invented the art of giving Christmas presents. This is what the narrator tells us in "The Gift of the Magi." In the Bible, the Three Wise Men brought gifts of gold, frankincense, and myrrh to the baby Jesus. As they were wise, the narrator thinks, so too were their gifts. Della and Jim, however, are unwise in that they've sacrificed for each other the greatest treasures of their house. But at the same time they're wise in that they give each other gifts that demonstrate their mutual love. It's not so much the actual gifts that matter in this case—which turn out to be useless, anyhow—but the spirit in which they are given. Therein lies the wisdom of Della and Jim, which is why the narrator says that they are the wisest of all who give and receive gifts.