This is a great book and it is lovely to see a question about it on this website. Mostly of course this book is studied in Britain, so questions about this novel do not come up very often!
There are many themes contained within this book that is often used for the British GCSE English Literature exam. You might find it useful to consider what the novel says about each of the following:
Family relationships: Clearly Billy has a somewhat strained relationship with his brother Jud and his mother. The father is obviously an absent figure, and Billy is left to face the cruelty and lack of love expressed by Jud and his Mum, shown most clearly in Jud's killing of the kestrel and his Mum's complete lack of understanding of how important it was to Billy.
Education: Billy is shown to suffer some of the horrors of education, which involve corporal punishment and cruelty and very little education as we think of the word. Mr. Farthing is the one shining light in the school as he spends time with Billy and comes to understand him.
Poverty: Billy comes from a working class background and poverty is something that is always evident. He is not able to afford a sports kit and is shown in many ways to be neglected, both financially and emotionally. The tale says a lot about the inescapable fate of many children from working class backgrounds.
Hope these themes help! Good luck!