rel=”nofollow” is added to links to tell search engine spiders, in particular Google’s bots, not to follow a link which has been added in to a web page.
These links specifically tell search engines not to count the particular link for search ranking purposes, for example, if the link is pointed to URLs left by those leaving blog comments, and therefore, should not be counted as an “endorsement” by the site linking out.
Likewise, such links were historically good for external, untrusted links, though its debatable if they have a major role in the future of search: rel=”nofollow” links from high quality sources are worth having; dofollow links from low quality or spammy sites should still be discouraged.
In general, rel=”nofollow” should be applied to external links to untrusted sites – BUT – care should be taken never to link to untrusted sites, ever. So moderation is key.