What is Nofollow?
It is a meta tag that is added to the head section of your website page/s, or to then of a hyperlink. By tagging a website as ‘Nofollow’, it tells search engine crawlers not to follow any links on that particular website. If you tag a hyperlink as ‘Nofollow’, crawlers will not follow that link. The tag tells search engine bots not to follow the link, or attribute the links to PageRank to affect how those links appear in a search engine results page.
Keep in mind that the nofollow tag doesn't remove a site from Google's database. Google doesn't follow that instance of the link, but that doesn't mean the page won't appear in the Google database from links someone else created that haven’t been tagged with nofollow. Not every search engine honours nofollow links or treats them the same way. But major search engines Google, Yahoo and Bing support the nofollow tags.
How to use the Nofollow tag
For a webpage
<meta name="robots" content="nofollow" />
For a hyperlink
<a href="http://www.example.com/" rel="nofollow">Link text</a>
<a href="http://thisIsJustAnExampleLink.com" rel="nofollow">Your anchor text here.</a>
Why would you want to use it?
So, if you want to link to a something but not contribute to how that site ranks in search engine results, you would use the nofollow tag. It was originally created for use with pages with message boards or comment threads, to prevent spammers from linking to their sites to gain better rankings in search engines. It is also now used by webmasters and bloggers for affiliate or paid links, so as to not sway page ranking. If Google catches you passing PageRank from a paid link, they view it as spam, and you could end up being removed from Google's database. It can also be used to untrusted content, or ‘bad’ content the poster wants to show readers, but not promote it at the same time.