Hypertext fiction is a genre of electronic literature, characterized by the use of hypertext links which provide a new context for non-linearity in literature and reader interaction.
Do you remember choose your own adventure books? Hypertext games can work like that - instead of flipping to page 47 to open the door you just click a link. Hypertext works also include other forms of poetry and prose, and give both (or either) the author and reader power in deciding the pace of the story.
Twine is an open-source tool for telling interactive, nonlinear stories.
Twine is the program I use to create hypertext games. It allows you to save your works as an html file, ready for publishing online. I put together a resource guide for beginners, along with some game recommendations—you can find it on my ePortfolio blog.