What is Lady Snowblood about? Vengeance. Pure and simple, this is a revenge story.
Yuki was named as a child of hell by her mother. Yuki's father was killed by a group of men who conspired to use him to start an uprising; they then brutalized her mother. Her mother subsequently killed one of her attackers and ended up in jail, where Yuki is born. Yuki's mother was serving a life sentence; there was no way she could escape and continue her revenge. Consequently, she concocted a plan which included seducing the guards in order to produce a child who could pass beyond the prison walls.
Dying in childbirth, Yuki's mother impresses upon a friend the importance of imparting to her infant daughter the necessity of her revenge--the grudge that she could no longer carry, but which she passed to her daughter. The friend agrees to do so, and Yuki ("snow," so named for her snow-white skin) is trained to become the instrument of her mother's vengenace.
Twenty years later, Yuki is a skilled assassin. For the price of 1,000 yen she will perform murderous miracles, often proceeding through trickery, deceit, and the assumption that as a woman she poses as little threat to the criminals she is often dispatching.