This quote is both a melancholy reflection, and a subtle foreshadowing, of the circumstances of the Loisels in The Necklace.
Madame Loisel borrowed, and lost, a diamond necklace from her wealthy friend, Madame Forestier. They are loathe to admit the problem, and instead pay an incredible amount of money, far beyond their means, to buy a replica and return it without making any mention of the matter. By the end of the story, it has taken ten years, most of their work, and all of Madame Loisel's former beauty to repay the money needed to replace the lost necklace.
"How little it takes" at this point, may refer to the circumstances which changed their lives; a single evening, one mistake, and one responsibility they were unable to afford, has "broken" the Loisels and essentially ruined their lives.
However, this is also a bit of foreshadowing; the necklace turned out to be simple costume jewelry, worth virtually nothing. The Loisels have spent years repaying a debt that was never asked of them. In fact, it was their own stubbornness and pride that cost them so much; it would have taken but a little humility to admit to Madame Forestier that the necklace had been lost, and they would have saved themselves from a life of misery.
In terms of irony, this seems to suggest that the things we covet most are often the things that destroy us, and they can be so innocuous as to evade our consideration until it is too late.