Dofollow links are hyperlinks that tell the search engines to pass along their page rank to influence on outbound links. This factor affects a lot for SEO purpose. If you get more do follow links, then search engines will decipher your links as back links and you have more chances to receive positive values for your site's ranking.
Nofollow links are exactly the opposite. These hyperlinks don't have the ability to pass on a page rank status to other websites. Nofollow links don't consider as crawling links from search engines and so the link associated with Nofollow websites won't crawl by search engines.