Historical criticism, as the name implies, interprets a work of literature within the context of its time period and the life of its author. The Mill on the Floss is in many ways an autobiographical novel. Maggie, born around the same time as Eliot (whose really name was Mary Ann Evans), is similar to Eliot, while Tom is based on Eliot's older brother Isaac.
Patriarchy is one of the historical contexts that impacts both Maggie and Tom. Through both the legal system and cultural norms, men, considered innately superior to women both physically and intellectually, were given most of the power in mid-19th century England. Women were little more than property and society was organized to keep them within the web of male-dominated social and financial relationships. Therefore, although she is very "quick," or intelligent, Maggie is not given the same educational opportunities as Tom—such as the chance to learn Latin—specifically because she is a girl and girls were pre-judged not to have the same depth of intellect as males. Tom is less intelligent than Maggie, but is given more opportunities, power and responsibility because of his gender.
Further, like Eliot, Maggie steps out of the strict gender boundaries established to keep women under the control of their families. Maggie, like Eliot, transgresses against Victorian (and pre-Victorian, as the novel begins around 1829) ideals of womanhood which valued docility, meekness, kindness, obedience, serving others selflessly, and quiet domestic attainments—and contentment with this lot. While Maggie, like the young Eliot, is deeply attracted to Christianity, an approved outlet for women, Maggie is also full of anger and seething emotions, anything but docile. As a young girl, for example, she expresses her anger by driving nails into her doll's head, re-enacting a story in the Bible in which the Hebrew woman Jael subverts domestic norms to drive a tent peg into the head of an enemy leader, killing him and becoming a heroine as a result.
Like Eliot, Maggie breaks sexual taboos when she floats down the river alone with Stephen Guest. He wants to avoid a scandal by marrying her, but she refuses. Eliot herself got involved in a long-term unmarried relationship with George Lewes, a married man, highly scandalous for that time period. Like Isaac with Eliot, Tom sharply repudiates Maggie for her actions.
Overall, both Maggie and Eliot are stunted by the historical period in which they live because of the rigid gender roles that ignored the reality of individual personality and intelligence.