Theedge is the development branch of Lunar, a set of tools that allow you to install, remove and upgrade packages. It also comes with several other tools to help you selecting packages and finding out information about their status, files etc. For more information about how theedge works, read the lunar page.
The development fixes and new features go into theedge exclusively, so that they can be tested without bothering users who don't want to run developement code. You should install lunar if you don't want this. However, many bugfixes go directly into theedge, so sometimes you might want to switch to theedge instead.