This shows how your sites are connected. The top section lists your other sites that are connected to the URLs you entered ("me" links). The 'Score' column shows how well-linked each is - green for fully linked, red for just one. 'Possible connections' is a list of other sites that link to your URLs with 'me' links.
These are public links on websites, marked up using Open standards such as XFN and FOAF, designed to express relationships online.
To use XFN to connect sites, add rel="me" to your link like this:
<a href="http://kevinmarks.com" rel="me" >me</a>
To use FOAF, create a FOAF file and link to it from your web page. More details on FOAF.
The Social Graph API makes information about the public connections between people on the Web easily available and useful for developers. Developers can query this public information to offer their users dramatically streamlined "add friends" functionality and other useful features.
For more information, please visit the Social Graph API FAQ.