In his short story "The Gift of the Magi," one thing author O. Henry is criticizing through satire is materialism.
In the story, both Della and Jim are deeply in love as a young married couple, but they are also very poor. Due to their poverty, Della feels heartbroken that she has only $1.87 to buy Jim a Christmas present. She wishes she could buy him something special, "something fine and rare and sterling--something just a little bit near to being worthy of the honor of being owned by Jim." Her desire to want to buy Jim something special, "something worthy of the honor of being owned by Jim," shows that she equates honor and worth with material possessions. In her mind, Jim is worth great value, and Jim needs possessions of great value in order to show off his merit. In addition, she equates demonstrating love with material possessions.
Further evidence that not only Della but Jim places great value in material possessions is seen in the fact that Jim's most valued treasure is the gold pocket watch he inherited from his grandfather. For Della, her most valued material possession is her hair.
Ironically, by the end of the story, we learn that both characters sold their own treasured material possessions to buy for the other character an object they feel honors the other person's most valued material possession; i.e. Jim sold his watch to buy Della hair combs, while Della sold her hair to buy Jim a fob for his watch. The irony of the story helps satirize society's materialism. If neither character had associated love and honor with material possessions, the story would not have come to such an ironic conclusion. Since Western culture is a very materialistic culture, it is due to society's influence that Della and Jim think only in terms of material possessions. It is this aspect of Western culture that O. Henry is criticizing through his satire.