The narrator, simply put, is the "person" who tells the story. The story's narration
is the viewpoint from which the story is revealed.
Sometimes the narrator is involved in the action of the story, in which case the story is written in the first person point of view — I, me, my, mine. For example, Harper Lee's To Kill a Mockingbird is told in first person from the viewpoint of Scout, a young girl. Her view of the world, and thus the narration of the story, is limited by her age and inexperience. Although she may not always understand exactly what is going on, she explains what she sees and feels — and you are left to apply what you know about history and the ways of the world to better understand what's really going on in her community.
More often, a story is narrated by an unidentified entity and written from the third person point of view — he, she, they. When a story is written in third person, the narrator may be omniscient — privy to the thoughts and motivations of every character — or limited — knowing the thoughts of only a single character. Ray Bradbury's Fahrenheit 451, for example, is told from the third-person point of view, but the reader is limited to the thoughts and emotions of only the main character, Guy Montag. The motivations of the other characters are revealed only secondhand, through the biased observations of Montag.
A story's narration can also be written in second person, using the pronouns you and your. This style isn't used very often, and is used more often in poetry than in prose, but it can be an effective storytelling tool. Jay McInerney's bestselling Bright Lights, Big City is a novel written in second person. He chose to write it this way to make the trials and tribulations of the unnamed narrator more intimate and personal to the reader.