The central idea of a piece of literature is essentially what point or message the author is trying to convey with his / her writing. Central idea is often referred to as theme. In order to figure out the central idea or theme of a piece of literature it often helps to ask yourself two questions.
1) What is the piece of literature about (topics)?
2) What is the author saying about these topics?
The answer to the second question is often going to be the central idea or theme of that literary piece.