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 his head." The right to make decisions about what events will be narrated and by whom is called the authorial privilege.
Sometimes, someone will be the author and the other the narrator. For instance, the GM may decide how successful an attack is after the player states they are attacking. The player is the narrator and the GM is the author. Once the GM states whether the attack misses or hits, the player might describe what the attack looks like. For another example, a player may declare his character is attempting to charm someone. The player is the author, the success of the action may be partially delegated to the system, and the GM narrates the failure or success.