What does it mean to say that somebody believes something?
I think that a belief is a mental state, representational in character, taking as its content something that could in principle be stated as a proposition. To believe p is to hold that p is true.
How can we distinguish between believing that we hold that p is true and actually holding it to be true? Beliefs predispose us to certain behaviours. If we consider what people actually do, we can sometimes discern a difference between what they profess, and what they actually believe.