You could also write about the themes of the book. One theme is the belief that something good can be found even in an event that's wrong, senseless, or sad. Christy's search for the meaning of life renews her faith in God, giving her the strength she needs to be able to rise to the challenges of the future. Another theme is the characters' search for their own identity. This teaches them to respect the values and beliefs of people who are different from themselves. Christy must learn not to stereotype the people of the Smoky Mountains. A third theme is the need for people to learn to accept and understand death as a part of life. Christy is devastated when Fairlight Spencer dies, and she turns to Alice Henderson, a Quaker missionary.
You could also write about the social issues in the book. The people who live there are poor and illiterate. The conditions under which they live are primitive and challenging, and some of them hate outsiders so much, they threaten violence against Christy. They are deprived in every way a culture can be, socially, economically, and educationally. The people are suspicious of modern medicine and believe in superstitious folk lore.
You don't say whether you have a specific topic for your essay, but if you do, don't hesitate to ask for help. Good luck!
Basically, this book is about the character Christy Huddleston and the experiences she has when she goes to teach in a very rural area of Tennessee. The link below gives you a brief summary of the work and may help you to gather some thoughts to begin your essay. The book lends itself to a comparison/contrast essay because of the way it is written. You could compare the life Christy used to live with the life she experiences in Tennessee. Or you could compare and contrast the different characters she encounters in Cutter's Gap and how she interacts with them. The book is lengthy but it is rich in development of character and setting.