Sometimes called Choose Your Own Adventure (CYOA) – although apparently there’s some trademark problem with using this term generically, it’s an interesting format that seems ideally suited to the web and to mobile devices.
It’s simpler than Interactive Fiction (IF) which requires typing in commands and is thus not so intuitive for new users. Also it’s probably not well-suited to mobile devices.
A very interesting new tool, Inklewriter, is available for free, and it’s easy and a lot of fun to use.
Here’s my first attempt at a simple story using this tool.