As you say there is a problem in the short story. The main two characters, Della and Jim are poor and they want to express their love to each other in the form of gifts for Christmas. However, both lack money as they are barely getting by.
They both have one prized possession. Della has her beautiful hair and Jim has a gold pocket watch. They, of course, love their prized possessions, but they love each other more. So, Della cuts her hair and sells it. She buys a chain for Jim's watch. Jim, in the meantime, sells his watch and buys combs for Della's beautiful hair.
In the end, they have gifts that they cannot use. However, through their act of sacrifice, they demonstrated incredible love and sacrifice. For this reason, O. Henry call them wise. It is better to give than to receive is the moral of the story. And consequently this is how they overcome with love.