The narrator is the person narrating the events in the fiction of a role-playing game. The GM is the primary narrator in a traditional game. However, a player narrates when they say, "I cut off its head." The right to make decisions about what events will be narrated and by whom is called the authorial privilege.
In role-playing games, some people make a distinction between the narrator and the author in a scene. In these cases, the author makes decisions of what happens in the game world (perhaps by interpreting the game rules), and the narrator then describes what happens in the game world according to the author's decisions. For example, a player decides that their character will attack a monster and describes how they try to do that; they are both the author and narrator. Next, the GM decides how successful the character's attack is, and allows the player to describe the scene according to that success; here, the GM is the author and the player is the narrator.