According to enotes literary terms guide, hubris can be defined as "arrogance, excessive self-pride and self-confidence." The guide goes on to say, "The word was used to refer to the emotions in Greek tragic heroes that led them to ignore warnings from the gods and thus invite catastrophe."
This description fits Mathilde fairly well. She has too much pride, so much, in fact, that she would rather destroy her life than admit she had made a mistake. Mathilde is lower middle class and is ashamed of that status. Though she is young and beautiful and would probably be well-liked for her good qualities, she is unhappy and wants to be the envy of others. She insists her husband buy her things beyond thier means and borrows what she thinks is a very expensive diamond necklace to show off at a high class affair. When she loses the necklace, she buys a replacement rather than admit her error, and the replacement is so expensive that she must work for years to pay for it and move into a seedy area to save money. One might argue that these actions are prompted by shame and not pride, but they are actually a result of her desire to be better than others. She desires the finer things because she feels superior to her lot in life and thinks both her husband and her status are beneath her.
In the end, she meets her friend, Madame Jeanne Forestier, from whom she had borrowed the necklace and pridefully boasts that she is the stronger, better person for working so hard to replace the necklace. The irony is that she has destroyed her life for nothing...for pride alone, since the necklace was a fake.