When Della presents Jim with his Christmas present--a platinum fob chain that "surely had been made for Jim and no one else"--he catches the reflection of Della's "bright and ardent spirit" in the chain's reflection and falls down on the couch, smiling. He suggests that the pair put away their presents because they are "too nice" to use at the current moment.
This reaction occurs because the couple's gifts to each other have come at a great sentimental cost: Della has cut off her beautiful hair to afford the fob chain for Jim's watch, and Jim has sold the watch in order to purchase a delicate set of combs for Della's flowing locks. Because of these sacrifices, the new Christmas presents are ultimately useless; Della's hair isn't long enough to wear the combs, and Jim no longer has a watch to place on the chain.
Despite this, Jim understands that these circumstances are irreversible and instead chooses to honor his wife's generosity. He realizes that the love that the two share is of far greater value than any tangible gift they could exchange.
Jim reacts in complete disbelief and almost in a laughing manner. The poor guy has just come home to find his wife has cut off all her hair, and he's probably thinking something like, "I just sold my watch to get her those combs...sigh!" Then he finds out why she cut her hair - to buy him the watch chain for a watch that has been sold!
He realizes that there's no point in being upset about the turn of events, and he also realizes that he is a very lucky man to have such a loving wife. He realizes that they are truly rich, despite their poverty.