Interactive Fiction is a new narrative medium that grew out of the early "text adventure" games. (That's where the name TADS comes from, by the way: it's the Text Adventure Development System. "IFDS" just wouldn't be as catchy.) In a text adventure, the player takes the role of the protagonist. The game proceeds as a dialog between the player and the computer, rendered in conversational English text (or in another human language), with the computer describing the situation and the player saying what the protagonist should do next. As the old marketing spiel put it, you don't just read the story, you become part of it.
If you've never played or seen a text adventure or Interactive Fiction first-hand, a sample transcript might make the idea more concrete.
The early text adventure games were decidedly games, with the focus on challenging the player with a series of puzzles and riddles. But the form these games took, as explorations of simulated worlds through prose seemingly written on the fly in response to the player's actions, suggested the potential for something more than just a computerized puzzle book. These games told stories, in a new and different way. This new kind of story isn't the static narrative of traditional literature, but a dynamic collaboration between author and player that never unfolds exactly the same way twice.
Commercial text adventure publishers such as Infocom started exploring this territory with their later games. But their explorations were cut short by changes in the industry, which was rapidly shifting to the modern notion of a computer game as a multimedia experience; the text game publishers were squeezed out financially just when they were hitting their artistic stride. But they left behind a fan base who weren't merely nostalgic for the text adventures of old, but also recognized the format's potential as a serious artistic medium, and had the technical skills to carry on with new post-commercial works. Enthusiasts have been exploring that potential ever since, steadily expanding the medium's boundaries.
Today we call it Interactive Fiction because the term better captures the scope of the medium. The defining feature of IF is still the text-centric, conversational style of play, but IF today can incorporate graphics and sound. Many modern IF works are still game-like, but many others are not. Some IFs are non-linear stories, some are character studies, some are sculptures in words. Even with a few decades of history behind it, the medium is still full of surprises, and many feel that we've only scratched the surface of what it can do.