A dynamic condition between a group of two or more agents/systems, where each has the potential to change another member of the group in a meaningful way.

Interactivity is to games as sight is to visual art, and as sound is to music; games presuppose interactivity just as deeply as music presupposes the ability to hear.

Yet term is widely misused. To use some example from Chris_Crawford?, if a tree limb falls and you avoid it, that is not interactivity, it's reactivity. Movies aren't interactive either:

"If the movie were interactive, you might see hour heroine pause and say "Gee, I think I heard somebody in the audience urging me not to enter the dark house. I think I'll take that advice." But this never happens! The protagonist always does that stupid thing that you or I would never do in a million years." ["Chris Crawford"]

Interactivity requires two or more active agents. According to Chris_Crawford?, it requires two or more entities which perform the functions of Listening?, Thinking?, and Speaking?. These entities may be human (as in board games, dice games, sports games), or they may be a computer (as in videogames). These can also be thought of as input, processing, and output.

Interactivity requires all three exist in every interacting entity. If one or more are absent, there is no interaction.

For example, books are not interactive. A book can't "listen" or "think", it can only "speak". A wiki, like this one, however, is interactive. You can read it, think about it, and make changes, I can go back and read the changes, think about them, and make new changes. It's not exactly a game, but it's an interaction between the authors.

According to Chris_Crawford?, good game design is a matter of making sure all three aspects of the interaction are done right, and work with each other. Preference should not be given to solely output (graphics, sound, music) nor solely to input (the user interface, the actions possible to the players), nor solely to process (the algorithms and rules that make up the game), but all three conjointly must be attended to. His assertion is that most bad game designs (any type of game, not only computer) suffer from a weakness in one or more of these three elements, and that the best game designs respect all three as essential considerations.

Reference: The Art of Interactive Design, by Chris Crawford. No Starch Press, 2003.