The Magi referenced in O. Henry's short story are the three Wise Men who brought gifts of frankincense, gold, and myrrh to the infant Jesus in the Biblical tale; this was a risky gesture, as it could have resulted in punishment by King Herod. Their travel and actions involved sacrifice and the act of selfless giving.  

Thus the narrator of this story compares Della and Jim to the Magi out of respect for their own personal sacrifices. Having no money to purchase each other Christmas gifts, Della had cut off her greatest treasure--her long, beautiful hair--in order to afford a chain for Jim's watch, and Jim had sold his most valued possession--the aforementioned watch--to buy tortoiseshell combs to adorn Della's hair. Much like the Magi honored Christ by falling before him with offerings of love, Della and Jim have done the same by showing no concern for their own desires or interests. They are focused only on the act of spreading love to each other. 

Della and Jim are compared to the Magi because, like the original three kings, this young woman and young man have sacrificed valuable and precious possessions of their own and given them willingly. All their acts are made from pure love and adoration.

O. Henry injects his authorial comment that Della and Jim "are the Magi" at the conclusion of the story after noting that

...two foolish children in a flat...most unwisely sacrificed for each other the greatest treasures of their house.

At this point O. Henry draws parallels between the three wise men and the young Dillinghams as they all have unselfishly given away their most precious gifts. And yet, the author declares that the young couple are the wisest of them because they truly understand the meaning of love that asks for nothing in return. Indeed, they are "the Magi."