We are given better definitions of these characters from their setting and surroundings. Right away, we realize that Jim and Della are leading a rather meager existence, as their home is not lavish, and their words and actions are those that are typically associated with financial struggle.
Even with the state of near-poverty that they are living in, however, Jim and Della both find it within their hearts to sacrifice what is dearest to them for the sake of the other person's happiness -- Della sells her hair, Jim sells his watch, and ironically, the gift that each receives has to do with the very thing they sold for the other person's pleasure (Della gets combs, Jim gets a watch chain). Through the settings, characterizations, and plot of this story, we are shown the true nature of both Jim and Della.
Both of them are self-sacrificing and selfless. Della gives up her beautiful hair (which is alluded to as hair that the Queen of Sheba would envy). He gives up his most prized possession (his golden watch--which would have been envied by King Solomon) to buy something for her. Both characters have the same qualities. Both are willing to give up their most prize possessions to make the other happy. Their love is so strong that their possessions don't mean as much as giving the other person joy. O. Henry defines them by their selfless actions.