It is ironic that Mathilde, who prides herself on her beauty and who requires expensive things to feel truly elegant, chooses a cheap imitation diamond necklace to complement her dress—and doesn't even realize how little it is worth.
When Mathilde asks her friend, Madame Forestier, to borrow some jewels, Mathilde is offered her choice of jewelry. After searching through her friend's box of jewels, Mathilde doesn't see anything she likes, even though she is offered jewelry "of exquisite workmanship." Unsatisfied with her options, she asks Madame Forestier if she has anything else. When she is presented with the "diamond" necklace, Mathilde is so exited that her "heart [begins] to beat covetously." Her hands tremble and she can barely lift it. Mathilde embraces her friend for her generosity in loaning her this exquisite necklace and is filled with ecstasy over the sight of the jewels around her neck.
Yet the "diamonds" are cheap replicas and are comparatively worthless. Though the jewels make Mathilde feel beautiful and elegant, they hold almost no value. Thus, the emotions that they elicit are ironic; Mathilde feels that the necklace makes her worthy of attending the ball, yet she is elegant and graceful despite the fact that she wears worthless jewels.
Mathilde believes that she was destined to enjoy the luxuries of life, yet she fails to demonstrate an ability to recognize authentic jewels from cheap replicas. This is an ironic twist that costs her the very beauty that she takes so much pride in early in the story.