There was clearly nothing to do but flop down on the shabby little couch and howl. So Della did it. Which instigates the moral reflection that life is made up of sobs, sniffles, and smiles, with sniffles predominating.
O. Henry evidently wanted it to be understood that Della was not crying because she didn't have enough money to buy her husband a Christmas present; she was crying because this was the last straw. She was crying because of the hard lives she and her husband had to lead on an income of twenty dollars a week, with eight dollars of it going for weekly rent on a shabbily furnished flat. Their plight was symbolized at the moment by the fact that she couldn't even afford to buy Jim a nice present after saving up pennies, nickels and dimes and the whole year. But she was really sobbing for her whole life.
O. Henry often wrote about the hard lives of the lower classes. Some of his best-known stories are tinged with sadness. In "The Furnished Room" a young man commits suicide in the same room where the girl he has been searching for had killed herself in the same way a week before. In "The Last Leaf" the sick girl called Johnsy manages to survive, but the old painter who saved her life dies of pneumonia. "The Cop and the Anthem" is about a man who is trying to get sent to jail so that he won't freeze to death while sleeping on a park bench during a New York winter.
Percy Bysshe Shelley wrote in his "Ode to a Skylark":
We look before and after,
And pine for what is not:
Our sincerest laughter
With some pain is fraught;
Our sweetest songs are those that tell of saddest thought.
The quote means that life has its ups and downs, "sobs" being the times when we face trials and "sniffles" when we face the more trivial matters that affect us, but not enough to utter a sob, and "smiles" which are the happy times in life when we enjoy what we're doing and who we're with. The quote leads the reader to believe that in Della's life the sniffles are what she predominately deals with in her day to day. She isn't entirely happy with her life as it is, she is far from content. She and Jim act as though they are in a higher station in life because that's what they aspire to. Since they aren't content it's easy to see why "sniffles predominate".
The quote you're referring to is written:
"There was clearly nothing to do but flop down on the shabby little couch and howl. So Della did it. Which instigates the moral reflection that life is made up of sobs, sniffles, and smiles, with sniffles predominating."
O. Henry's short story is a reflection on the pardoxes of life. The two characters, Della and Jim, sacrifice their personal loves (Della her hair, Jim his watch) so that their beloved may have something of value. However, Della cuts and sells her beautiful tresses in order to buy Jim a chain for his pocketwatch. Jim sells his watch to buy lovely combs for Della's hair. When the two exchange their gifts, both are useless, of course. The sobs come when they must give up something dear to them personally; the smiles are a result of learning of the love each has for the other. Though they have lost material items, and cannot benefit from the largesse of the other, Jim and Della have something much more valuable than these tangible items: they have the reality of love.
It simply means that life is full of sadness.