Interactive fiction, in the broad sense, is all fiction presented in such a way that the reader influences what text she gets to read. Two well-known examples are hypertext fiction, where the reader chooses between different links that she can click to progress through a non-linear story, and so-called "Choose Your Own Adventure"-novels, which give the player choices like: "If you want to hit John, go to page 34; if you want to apologise to him, go to page 56."
In the narrow sense in which I mostly use the term, interactive fiction is the medium of parser-based fictions with a world model. "Parser-based" means that the reader/player types in text commands, such as "go to the cathedral"; a piece of interactive fiction has a world model if it keeps track of changes in the fictional world, such as the positions of items and the moods of characters. This kind of interactive fiction is also know as "text adventures", though I highly prefer the former term: "adventure" sounds like a genre, but we are talking about a medium here.
On this site, you will find the interactive fiction I have written by clicking on "My Games" in the menu to the left.