From IFWiki

1) In conventional prose, a persona or "voice" created by the author in order to tell the reader what happens next (see plot). The narrator may be the protagonist, a participant in the action, an observer of the action (from a vantage point within the world of the story), or an external, omniscient figure.

2) In interactive fiction, the "I" who says "I didn't understand that" in response to half the stuff the player types; often considered the "voice" of the parser.

The IF narrator must not only describe the plot, but also help the reader keep track of objects that are in scope, the player's inventory, and implement various meta-commands (such as saving and loading games, disambiguation, etc.).

Crowther and Woods's Adventure features a benevolent, omniscient narrator who addresses the reader directly. More recent IF that plays with the function of the narrator includes Plotkin's Spider and Web and the "Wendy" sequences of Cadre's Photopia.