There are many Universal themes at Magi. First, is humbleness, as the couple (who are obviously Victorians) cannot do what the rest of society does when it comes to trying to keep up with the upper crust and be one of them: This couple is doing the exact opposite and understanding their circumstancial position.
Then, there is love, of course, in the shape of sacrifices.
There is also humility- way different than humbleness- which means the capacity of accepting defeat without feeling humilliated.
All these topics are written within the concept of an excessive society where the exact opposite is going on.
Author's Purpose is another way of asking you what the theme is in a story. The theme, or lesson in this case can be summed up in fairy tale fashion: "Be happy with what you have."
Della and Jim both love one another deeply, and yet this is not enough of a gift. O. Henry suggests that this couple is consumed by material things, and that when affection is bought instead of earned, an unfortunate end occurs.
Della's one true prized possession is her hair; Jim's prize possession is his pocket watch. Because of their adoration for one another, both sell off their possession respectively.... and O. Henry makes the end result ironic and twisted.
Without her hair, Jim's gift of the combs to Della are useless; without the Watch, Della's gift of the chain to Jim is equally without purpose. All we are left to deduce is that the love for one another is greater than any gift.
This is most likely O. Henry's intent. The religious connection is quick: The Magi (if you don't know) were the wise men, who were showered with gifts following their journey; the gifts, naturally were material, and refused... because the best gift was the intangible: love, respect, recognition.
Della and Jim both love honor and obey one another thus making them the perfect married couple... O. Henry suggests that because they have no money, and no prized possessions any longer, that having one another is truly the Gift of the Magi.