Most of the time, the reader can safely assume that the writer tells the truth. That what appears on the page is an accurate version of events in a story. This is not meant to suggest that characters do not tell lies to each other, or that the events themselves are plausible, merely that what is written on the page did in fact happen in the story.
There are, however, exceptions to this rule. The author can deliberately lie to the reader by relating events on the page, only to reveal that those events never actually happened in the story. The narrator of the story becomes unreliable.
As an example, consider the movie, A Beautiful Mind, in which the principle character suffers from