If something rests on a particular idea, belief, or fact, it is based on it or needs it in order for it to be true.

Christianity rests on the belief that Jesus was the son of God. 基督教的基本教义信奉耶稣是上帝之子。

to depend on someone or something

Our success rests on an increase in sales. 我们的成功取决于销售量的增加。