FirstMagic Widgets are small web apps you can install in the Menu, Sidebar, or SiteFooter of the site, to add special features to your pages - like Social Media functions, various Google Services, and so on.
One example is the Twitter feed in the Blog Sidebar; you can change the feed by going to the Sidebar container and open it - then point the URL inside to a different Twitter page.
Another example is the four Homepage buttons: it is a Widget attached to the Homepage that lists the four newest Web Pages in the Layout you point it to. It will also grab the first image inside those pages and use as buttons.
Widgets can be attached to any page or number of pages.