It means that the protagonist was in a state of confusion where he/she didn't know what to believe about him. Thus, he/she may have alternated between believing everything and believing nothing.

Mark has a good answer, but let us consider further this "everything and nothing". It means that someone has an enormous reputation. It also means that it is difficult, on the basis of a glut of talk about this person and their reputation, that it is almost impossible to know what the truth is. The abundance of information produces a contradiction in terms, which is what is presented to us. So it is a convenient expression for a person to use with us, when they inform us that we should believe "everything and nothing" at the same time. It shows us how puzzling information about someone can be. If we cannot determine the truth, we are left with a puzzle or a "conundrum". Another term which alludes to an ancient story is to refer to this as a "Gordion Knot". Alexander the Great "solved" the puzzle of the "Gordion Knot" by cutting it in half which his sword. But when we say "believe everything and nothing" we are proposing that we don't have a sword sharp enough to sort out all the things we hear about someone. So, we make a joke of it, and suggest that others "believe everything and nothing". It is a blunt contradiction in terms.