That's a root-relative link. It's a relative link (somewhat akin to ../) but it begins at the root of the site. If a page three levels deep on the site begins a link with the forward slash, the remainder of the path will be relative to the root of the site.
A benefit to this form of pathing is fewer characters in the markup:
http://example.com/page.html
vs
/page.html
Another advantage is portability across domain changes. If example.com content is moved to example.org, for example, root-relative links will still work, assuming the same directory naming/layout is used. Especially useful if developing pages locally, then uploading to the web.
As with other types of pathing - relative (../) and absolute (http://...) this is still subject to updating links when files or directories are renamed or moved.