dofollow is normal link without any attribute. In HTML code it looks like:
Code:
<a href="http://site.com">site</a>
on other hand nofollow link has an additional parameter "rel" with attribute "nofollow":
Code:
<a href="http://site.com" rel="nofollow">site</a>
Nofollow link tells google not to consider visiting linked page. It is used for example when one is linking to a not trustworthy site or when this is a paid link/advertisement or for example an administration/login page.
Here is explained what are nofollow links regarding SEO: http://internetlifeforum.com/seo-search-engine-optimisation/187-nofollow-links-good-seo/
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