The allusion to the Magi of the Bible, extends to the idea that these men traveled from afar to be in the presence of the greatest gift of God to mankind, His only Son:
For God so loved the world that He gave his only begotten Son, that whosoever believeth in Him, shall not perish, but have everlasting life. [John 3:16]
Clearly, O. Henry's story is one with a very Christian theme, the theme of love as meaning that one is willing to sacrifice one's own desires for the happiness (or safety) of another. Like the Magi, Della and Jim understand the true meaning of love, and they understand that sacrifices are often necessary in order to experience true love. Like the Magi who traveled from great distances under strenuous conditions, Della sacrifices her prized possession of her luxurious hair in order to buy a present for Jim, and Jim does likewise for Della; in the end, they give each other the richest gift of love, just as the Magi bring the baby Jesus rich gifts.
The magi are significant for two reasons. One is that the use of the term shows that Jim and Della are truly wise. The other is that using the term is a bit ironic.
The term is ironic because the wise men in the Bible were these really rich people who could afford really expensive and wonderful gifts. By contrast, Jim and Della are quite poor.
The magi are also significant because using their "name" enables the narrator to talk about how Jim and Della are truly wise because of the way they show their love.