Hello,
A no follow back link is opposite to a do follow back link. No follow links prevent search engine's spiders to crawl the link. So, if you are getting a back link from a no follow site, it does not pass the link juice. No follow links prevent web spiders to crawl the link only humans will able to follow the link.
Do follow is an opposite to no follow link. Do follow link gives us link juice and back link. It tells search engines to navigate on the specific link. Do follow links are useful in bringing search traffic where no follow brings referral traffic. Do follow links are too much helpful to improve a site's PageRank.
Thanks and Regards
Richard Smith