'dofollow' is the default setting for the bots anyway so it's pointless. 'nofollow' tells them not to follow links on that page (assuming that you're using this in your meta tagging?)
NO-follow Tag - if you are using this tag in your meta that it indicate to spider don't index that page if you are using this tag for any outbound links then google doesn't read that links mostly affiliate sites are using this links on there affiliate links and Do-follow tag is indicate spider to follow this link if you are getting link from do follow blog or website then it will be become your site back links b'coz google read that links and on the other hand if you getting links from no-follow page then it's mean you can' get backlinks from that page.
Simply Means: Do Follow-Spiders follow and index that link(site page). No Follow-Spiders dont follow and index that link(site page).