Twine is essentially a program that organizes web pages that will allow you to write non-linear stories, share prototypes and even animate short poems. It is a simple interface that begins with a selection of archived projects.
Once you click +Story on the right, you are presented with a blank window. From here, +Passage will create a passage, which is basically a page of your story/prototype/etc.
Twine lets you conveniently edit these two for your story from a menu on the bottom left: