/ is where the anchor link is going to take the user that clicks on the link.
/ will take the user to the domains root, or homepage typically. In other words, if your domain was example.com, the link would take you to whatever page displays at http://example.com/
The advantage to using / is that the anchor links using it will still work if you move your websites files under a different domain name. Plus it is shorter than typing out your domain name every time.
From what I have read it is just older search engines that get confused by relative links like href="about/us". I think the trick there used to be to always start your links with /.
If it really concerns you, do a search for something like "SEO absolute vs relative links" and you should find some more in depth information on the pros and cons of such.
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