The quote you have identified is uttered in the form of a prayer by Della after she has cut off her hair to gain the money she needed to buy Jim the watch fob that she feels is a fitting present for her husband whom she loves so much. However, as she hears his step on the stair ascending to their appartment, she suddenly begins to worry about Jim's response to her new hair style, as we are told that her long, lovely hair was her pride and joy. Note how her hair is described:
Had the Queen of Sheba lived in the flat across the air shaft, Della would have let her hair hang out the window some day to dry just to depreciate Her Majesty's jewels and gifts.
It is compared to a "cascade of brown waters" and is clearly something that both Della and Jim place incredible value in. Thus, as she hears her husband coming up the stairs, Della suddenly has a moment of doubt as she wonders what the consequences of her sacrifice will be. The quote thus identifies a moment of self-doubt as Della questions if she has done the right thing and wonders how Jim will respond to the radical change in her personal appearance.
Della says it to herself just as her husband Jim is about to walk through the door. She says it because she has cut off all of her hair and has sold it to buy Jim a Christmas present. Her hair was her most prized possession, but she gave it up selflessly to buy Jim a present for Christmas. She tried to make her short hair look appealing to Jim by curling it and she's hoping that despite the fact that her hair is gone, he'll still think she's just as beautiful. She sold her hair to buy Jim a gold chain for his gold watch. Jim's watch is his most prized possession. It was passed down to him through the generations. However, he would always feel embarassed to take his gold watch out to check the time because it was attached to a leather strap. They were a poor couple just trying to make ends meet.
What Della doesn't know is that Jim has also done a selfless thing. She's about to find out after he walks throught the door just exactly what that selfless act is. She finds out that Jim has sold his gold watch to buy Della beautiful combs to put in her hair. Of course, once Jim walks through the door and sees Della's short hair, he realizes she'll have no need of the combs until her hair grows back.
It's situational irony. They no longer have need of the presents they bought each other for Christmas by giving up their most prized possessions. She has no need of the combs because she cut off her hair and he has no need of the gold watch chain because he no longer has the watch. The significance is that their love for each other is their most prized possession. That's what they find out through the experience. Material possessions are not what's important. The fact that they'd go that far to make each other happy is the most wonderful possession of all.