These days it's pretty common to see games with branching storylines, so different tools have been developed to design such games. Of course, you can use standard flowchart design tools (I'm actually using Visio for a project), but tools like Twine are nice because they allow you to see the flow of the game in real time.
Basically, Twine is a "flowchart for games" tool. You can create the different boxes with text, choices and events, and test the entire game to see how it works. You can add more boxes either manually, or by creating links in your existing boxes. In every section (or box) you can add images, video and audio, so you're not limited to text.
Being able to add different kinds of media is very useful since you can add rely on visual elements to describe events in the game, even if you use crude sketches. However, this can also be useful to take the entire project to a new level in case you don't like the idea of limiting the tool to an internal preproduction design tool. What do I mean? Answer coming below...
You can distribute these projects since the entire thing is actually an HTML document. This means you can share it with other team members even if they are in a different country. For example, you can share it with your music composer. Since Twine can add background music, you can test parts of your game in Twine, including music.
However, you could also use Twine to make a full game if you wanted. Some of you might be familiar with old text adventure games such as the Zork series. Yes, the last Zork games were in 3D (similar to Myst). However, the first Zork games were text-based games. These days, indie developers are making text-adventures again, so the genre is definitely not dead. Since Twine can add images, video and audio, you can make "text + images adventure games" easily. All you need is to think outside the box and realize these can be games as well (they certainly were in the 80s).
All the editing is done using code similar to HTML. The code is easy to use, so anyone used to HTML should have no problems. I have to admit that HTML and game development are two different things, so game developers should not be expected to know and use HTML. I think this would be my only problem with Twine. They could add simple editing tools to make it more user-friendly, instead of asking users to use code to do simple things like adding an image.
On the other hand, Twine can be very useful for preproduction, and can even be used to create a full short text adventure game. Twine is free, so you can download it and start writing interactive stories with it right away. If you do create your interactive fiction with Twine, feel free to show it to me via Twitter, or post it in the forums.