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.
The word magi is the plural of magus, which means wise man or even sorcerer (the English word magic comes from the same roots). It is an Old Persian word that was taken into Greek. In the Gospel of Matthew, expanded by later Christian tradition, the magi were the Wise Men who made a long journey from the East, guided by the Star of Bethlehem, to worship the newborn baby Jesus as King of the Jews:
On coming to the house, they saw the child with his mother Mary, and they bowed down and worshipped him. Then they opened their treasures and presented him with gifts of gold and of incense and of myrrh. (Matthew 2)
The Bible nowhere says that there were three magi, but since there were three gifts, this number was assumed.
The magi thus symbolize wise and devoted figures who bring precious gifts in the face of great difficulty to themselves.
The three Magi were three kings from the Biblical telling of the birth of Jesus. These kings brought gifts of gold, frankincense, and myrrh to the baby Jesus. The title The Gift of the Magi comes from these Biblical kings who came bearing gifts. In the O. Henry story, Della sells her long hair to buy a watch chain for her husband, Jim. Jim sells his watch to buy combs for Della. The story centers around their sacrifices and the gifts that they purchased. At the end of the story, O. Henry writes that the three Magi invented the art of gift giving at Christmastime. He also states that Jim and Della were the wisest of all. He adds that all those "who give and receive gifts" are wise because "they are the magi."
I'm assuming you posted this question in the literature section because you're reading something, such as "The Gift of the Magi," in which there is a reference to the Magi. While there are many older and disparate references to magi, the most common and modern use comes from the Bible in reference to the story...
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of Jesus's birth. The Magi are the wise men who, for years, had been studying the stars in order to discover the coming of the Messiah. After seeing a propitious sign in the sky (likely an alignment and intensity of stars), they journeyed more than a year and found themselves in Bethlehem in a rustic barn where they found Jesus. They offered this child king their famous gifts--gold (which was, of course, very valuable to a poor couple who was kind of on the run), frankincense (a heavenly scent and one worthy of a royal priest), and myrrh ( a kind of gum or resin often used in embalming, symbolic for He who died and rose again).
They are generally used as a symbol of sacrificial giving and of humility, as they unselfishly put someone else before themselves.
What are Magi?
The word "magi" means wise men. The term is used to refer to the three wise men who came from the east to worship the newborn Jesus in some of the Gospels.
The word is used in the title sort of as irony and also to refer to the idea that Jim and Della are actually wise.
The word is ironic because the wise men had really splendid gifts to give Jesus -- gold, frankincense and myrrh. They were clearly rich. But Jim and Della don't have hardly anything to give one another.
The word also refers to Jim and Della being wise for being so in love and appreciating each other so much.