Mme. Jeanne Forestier
Mme. Jeanne Forestier is wealthy. That's basically all you need to know. She's the rich friend: the person you turn to when you need something absolutely fabulous to wear to that ball next weekend but don't have the money to buy anything appropriate. That's Mme. Forestier's role in this story: she's that friend for Mathilde. It's also Mme. Forestier who reveals at the end that her necklace was false and thereby single-handedly triggers the twist ending.
Apparently Mathilde and Mme. Forestier have known each other for a while, since their convent days. Around the time of the ball, though, it doesn't sound as if Mathilde's seen much of her lately, because it makes Mathilde too unhappy to visit her rich friend and see the life of luxury that she's not living. It doesn't sound like they see much of each other after Mathilde returns the substitute diamond necklace, either. The two women most likely don't meet again until they run into each other on the Champs Elysées ten years later. Mathilde's too ashamed to let her friend see the poverty she's living in, and is afraid to explain why she became poor (since that would mean admitting she lost the necklace).