Hélène is "a simple housemaid", living a very modest life with her husband and daughter, who both take her for granted. One day, after watching a couple play chess in idyllic conditions, she decides to learn how to play.
Throughout the film, chess is very much a symbol for Hélène aspiring to more in life. At one point, while trying to teach her husband how to play, her eyes light up as she says "La dame est la pièce la plus forte... c'est fou hein?" which could be roughly translated as "The queen is the strongest piece on the board... crazy, huh?".
This single sentence seems to encapsulate the whole state of mind of our protagonist. On one hand, the idea that she could accomplish anything, even be great or the best at anything seems far-fetched to her, yet terribly enticing. She is on a journey towards self-realization that is both exciting and a little scary to Hélène and those around her.
Sandrine Bonnaire is absolutely amazing as usual, and succeeds in showing the state of mind of her character in very few words. Kevin Kline is great as well playing Dr. Kröger, the man who teaches chess to Hélène and develops an unusual and complex bound with her. There are lots of nuances in their relationship and again, in few words, we as viewers can sense a lot is going on. Tension, attraction, challenges.
Caroline Bottaro's direction captures very well Hélène's modest and quiet life and the implicit contrasts between social classes.
I recommend this movie. If you are not convinced yet, give Guy Bellinger's review (here on IMDb) a read.