An unreliable narrator is a narrator that cannot be trusted because his/her version of the story isn´t completely correct for various reasons, such as his/her mental state or the fact that s/he may not be objective.
The best example of an unreliable narrator is one who narrates the story from a first person perspective. Sometimes the readers know it from the very start of the story that the narrator is unreliable while other times this is revealed gradually throughout the story or even at the end of the story.