What is the critical appreciation of the book The Mill on the Floss?
You have asked a very broad question here. I have included some links below to the enotes study guide section of this novel that you can peruse at your leisure, but let me offer the following words of introduction. This novel is widely considered to be a bildungsroman, which means it focuses on one central character and their maturing process, tracing their life from childhood into adulthood and examining how they become part of the society of which they are born into.
Thus any appreciation of this novel has to focus on the journey of Maggie Tulliver, its heroine, as she struggles against her society. She is shown to be an intelligent and perceptive heroine who continually faces the conflict of resisting the narrow, stuffy and restrictive society she is born into and obeying the dictates of social norms and customs. This of course finds its expression later on in the novel in Maggie's intense desire to be loved and understood. Not receiving love and understanding from her family, and especially not her brother, Tom, she finds it in Philip and Stephen, though in the case of Stephen, pursuing her relationship is considered a scandal by society. The end of the story presents us with a character that seems so imprisoned by the urges to do what she wants to do and then to please others by doing what they would have her do, that death seems to be the only escape to this conundrum. Her death allows her conflicts to die with her, and also gives her the opportunity to be reconciled with her brother in a way that would have been impossible in life.