Interactive fiction refers to text-based adventure games. The game provides an environment with which you, the player, interact by typing commands. The game responds to your actions, often opening up new possibilities, presenting new challenges, and advancing the plot. Playing interactive fiction is like reading a book, but where you, the reader, get to decide what happens next (within the bounds set by the game's author).
If these were books instead of games, and you were going to read them on your computer, you would need two things: first, the file containing the text of the book (e.g. OliverTwist.txt), and second, some program that would allow you to read that text (e.g. Word or Notepad). Interactive fiction is exactly the same - you need a game file, containing the text of the game, plus an interpreter, which "runs" the game file and displays its text.
My games were written using a tool called Inform, which produces game files in a format called z-code. A range of z-code interpreters are available for just about every conceivable type of computer. This means you can play my games on everything from a supercomputer to a cellphone, which is the great advantage of the game file/interpreter system.
So now all you need to do is download an interpreter for your computer (I recommend Frotz), and you'll be able to play the games listed below, plus hundreds more.
If you want to find recommendations for other games to play, I suggest you visit The Best of IF or Baf's Guide. Have fun, and if you like my games, please drop me a line!