This novel contains a number of important themes relevant to African society but also to a number of sociological world trends, which no doubt explains its appeal. I am not going to give you a huge list of themes, but here are three to start your thinking off, and then you can identify other themes based on these ideas. Each of these themes would be suitable to write an essay on.
The character of the father, Eugene Achike, clearly suggests the dangers of religious extremism. His attempts to control his family's life, even going so far as mapping out every moment of his children's day, shows exposes controlling nature of such fervent belief. His frequent bouts of violence also call into question his faith, exposing him as a hypocrite.
Another theme is the contrast between traditional beliefs and Western beliefs in non-Western societies. We can see this contrast played out in the contrast between Eugene Achike and his father, Papa-Nnukwu, who is a kind loving man who follows the indigenous beliefs of his culture.
The concept of silence and its consequences is likewise examined. The time that Kambili and her brother spend at the house of their father's sister is crucial, as this family, although Catholic, is open and the members are able to talk about issues. It is a nurturing time for Kambili and her brother. In contrast, it is arguably the silence imposed on the family by Eugene that leads to his eventual demise.