In my opinion, this is a brilliant movie. It's suspenseful, moving, and fairly realistic. However, if you've read the book first, you will probably be sorely disappointed; as riveting as the movie is, the book makes it look like something from the original Walt Disney.
A nine-year-old girl in Japan is sold into slavery, as is her sister. Unfortunately, they're both serving different families. Each of them has a chance to become a geisha, or entertainer. ("The very word "geisha" means "artist," and to be a geisha is to be judged as a moving work of art.) Chiyo, the protagonist, gets into a lot of trouble at the hands of her okiya's [geisha house] resident geisha, Hatsumom, a cruel young woman who is envious of Chiyo's beauty. Hatsumomo forces Chiyo to pledge herself to her, in exchange for learning where 14-year-old Satsu, Chiyo's sister, was sold. Chiyo meets Satsu and the two girls plan to run away. However, because of some of the things Hatsumomo made Chiyo do, Chiyo's okiya is now bolted shut so nobody can leave. Chiyo tries to escape by climbing onto the roof and then back down, landing outside, but she gets badly injured and the cost of the doctor who is summoned is added to Chiyo's expenses--what she owes the okiya. (In those days it was custom to reimburse the okiya for one's purchase price.) Mother--Mrs. Nitta, the woman who ran the okiya--decided that Chiyo would never be a geisha and would only be a slave for the rest of her life.
One day, Chiyo is crying on a bridge when the Chairman of Iwamura Electric happens to walk by with two geisha on his arm on the way to the Spring Dances. He is kind to her and buys her a cup of sweet ice, and Chiyo falls in love with him. She prays that one day she might become one of the geisha on the Chairman's arm. This is made possible when Hatsumomo's rival, Mamaha, takes Chiyo under her wing.
That's the briefest synopsis I can give.