Zwift is an online training app for cycling (and running). If you have an account at Zwift, you can also use other web apps, such as Zwift Power and Zwift GPS. You connect these apps to your Zwift account using your Zwift ID.
Getting your Zwift ID can be a bit tricky. For some reason, Zwift is not simply listing it in your profile, but you can figure it out if you analyse the link of a downloaded activity (.FIT) file.
It can be much easier using a bookmarklet. A bookmarklet is a small tool that is installed in your bookmarks bar and that can do simple tasks, such as getting information from the current web page.