From IFWiki

A measure of the player's ability to affect the game world and/or the story. If, in a given game, the player can substantially alter the course of the story, or has significant opportunities to change the state of the game world, the game is said to have a high degree of interactivity. On the other end of the spectrum are games in which the player moves through a largely prefabricated story without participating much in the creation of that story; such games are sometimes said to be on rails.

Note that there are two sources of interactivity. One is the player's ability to interact on an immediate level with the simulated world -- a game with many complex objects for the player to manipulate can have a high degree of interactivity, even if the story is immutable (or nonexistent). The other is the player's ability to influence the overall direction of the story -- a game can be considered very interactive if the player has significant power to causing events to unfold differently, even if this power is exercised through actions abstracted from the directly simulated world.

-- OKB 2002/08/21