The NOFOLLOW tag essentially tells the search engine to not follow this link. The actual html looks like this embedded into a href link tag:

So, why would you want to NOFOLLOW something. The quick answer is, the pages that you don’t really care about (copyright, terms of service, privacy policy, etc) “steal” valuable “link juice” on a page. You would rather have more relavant pages get indexed. So many SEO and link development specialists recommend the NOFOLLOW tag be inserted in links that you feel are not as relavent. The following video warns of the dangers of the NOFOLLOW.

Dangers of Nofollow.

SEOmoz Whiteboard Friday – Dangers of Nofollow from Scott Willoughby on Vimeo.