This is an excellent story to prove that material possessions are completely worthless in comparison to love. The poverty of Jim and Della is stressed from the very first paragraph of this story:
One dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies. Pennies saved one and two at a time by bulldozing the grocer and the vegetable man and the butcher until one's cheeks burned with the silent imputation of parsimony that such close dealing implied. Three times Della counted it. One dollar and eighty-seven cents. And the next day would be Christmas.
Note the way that the amount Della has carefully saved this money, suffering the "silent imputation of parsimony" because of the way she has had to haggle so carefully. The amount of money is so precious to her that Della counts it three times. The reader clearly gets the impression that she is having to work very hard to save even this much, and yet it is so little.
Both Jim and Della make the classic mistake of trying to show their love for each other by buying presents that they cannot afford, and can only afford through sacrificing what is most precious to them. Although the end of the story makes it clear that some may consider them to be "foolish," the narrator of the story stresses that this sacrificial attitude in order to show love only gives them a place among the Magi. They show their true love for each other in their willingness to sacrifice their dearest material possession for the other.