Symbolism, Imagery, Allegory
There's not a whole lot of imagery or metaphor in this story. That makes the few Bible allusions stand out all the more. There's the whole "magi" reference. The last paragraph compares Jim and Della to the three wise men who, according to the Christian New Testament, delivered gifts to Jesus on the first Christmas (see "What's Up with The Title?" for more on this comparison).
In addition, there are two other Biblical allusions, both made in connection with Jim and Della's prize possessions. Della's hair is said to be so gorgeous that it would inspire envy in the Queen of Sheba. Jim's watch would have been the envy of King Solomon. Both the Queen of Sheba and King Solomon are famous figures from the Old Testament.
What do all three of these references have in common, besides being Biblical figures? Well, they're all royal, very rich Biblical figures. The magi are often said to be kings, and brought Jesus three very expensive gifts (gold, frankincense, and myrrh), while Sheba and Solomon were both powerful monarchs renowned for their wealth and splendor. The comparison of Jim and Della's possessions to those of Biblical figures helps bring out how precious those two items are to their owners; to Jim and Della they're treasures, which they give away. But that's not all the images of Solomon and Sheba do. By bringing them up, and by mentioning the magi, O. Henry creates a sharp contrast between their spectacular riches and the obvious poverty and Jim and Della.
We have to wonder why O. Henry would do that. Because ultimately the story wants us to think about what it means to be truly rich. Where it really counts, Jim and Della are as rich as Solomon, the Queen of Sheba, and the magi, because they love each other. Just like the magi and Solomon (both figures famous for their wisdom), they're also wise, as the last paragraph tells us.
The Biblical imagery also beefs up the story's credibility as a parable. By invoking the Bible at moments, O. Henry makes "Gift of the Magi" feel more morally weighty.