I help you do say clearly actually Backlinks are the incoming links to a wesite page. we called like this inbound links, inlinks, inwardlinks etc. This is an important role in search engine optimization; specially page rank. In that case DoFollow backlinks plays an important role. and no follow links are may be relevant to your postâ€™s context and can come from the sources which have a potential to generate high referral traffic
Dofollow links are the links which are followed by google bot, these links passes link juice which either helps you to improve in your sites ranking or affects its ranking whereas nofollow links don't pass link juice and they do not make any impact on your site besides passing traffic only.
A Nofollow backlink wont get any vote from the site and neither would that url be counted as a Backlink for your website and has no influence within the PageRank. A link to your site with a DoFollow tag can get a vote from his website and that link could be counted in your Pagerank as a backlink to your site.
According to me you might have heard about alexa rank and about Google PR. Do follow links are followed by Google bot and crawler and it may help in raising Page Rank but no follow links are those back links that will not be crawled by Google or pass juice but if those links are opened in a browser with alexa tool bar the will bring your websites alexa at a good level.
Google give value to do follow link and ignore no follow links so we need to work on do follow link sites so that we can get back links for our site and no follow links are also valuable for getting traffic for site but we need to use high pr sites with no follow.
Do-follow links are the links which are followed closely by google robot, these links moves link juice which both allows you to improve in your websites ranking or affects its ranking while no-follow links do not move link juice and they don't make any effect on your website besides moving traffic only.
Dofollow links will be the links which are followed by google bot, these links passes link juice which either really helps to improve in the sites ranking or perhaps affects its standing whereas nofollow backlinks don't pass url juice and they can't make any affect your site other than passing traffic only.