Please read this section carefully. Not understanding where your stories are saved can cause you to accidentally lose your work.
Stories in Twine 2 are saved to your web browser itself, not to the twinery.org web site. 1) This is the case even if you're running Twine 2 from a copy you downloaded to your own computer.
Because of this, if you use multiple web browsers or profiles on your computer, the stories saved to one browser will not be available to any other. (Likewise, an in-progress story using Twine 2 will not be available on any other computer.)
And more importantly, deleting your browser's history will also delete your stories. The exact option that will do this goes under different names in different browsers.
In Internet Explorer:
Yikes, right? The best thing to do to avoid these problems is to regularly archive your work with the Archive link on the right sidebar of the story list. This saves all of your stories to a file on your computer that can then be restored with the Import link on the same page.