I feel that there is a lot of confusion as too exactly what DoFollow and NoFollow links do and don’t do. A common misconception is that if something is marked NoFollow then search engines won’t follow the link at all. This, however, is not true at all, because web crawlers simply aren’t going to pass up a potentially content rich page because its NoFollow. However, this doesn’t mean that search engines don’t treat the NoFollow links different than Dofollow.

The real thing that the two types of links determine is the transfer of Page Rank or commonly referred to as “PR”. Page rank is how search engines determine how important a website is by counting the number of backlinks to the site. The idea behind this is that if your website has lots of other website linking too it then your website must have good and quality content, so it should be ranked higher in the search results. The higher number of backlinks you have to your site the higher Page Rank you will have.
NoFollow links are basically links that search engines don’t count as a backlink. This is a common practice on High PageRank sites because the higher the PageRank of the site linking to your the more it will affect your PageRank.
DoFollow tells the search engines to count the link as a backlink to the site and thus gives the site being linked to a higher PageRank based on the PR of the site linking to it.
Many sites on the web now use NoFollow links because of automated bots designed to browse the web and post links as an attempt to build backlinks to a certain domain, usually of questionable content.