NoFollow Links are backlinks that do not count towards the page that it’s linked to’s ranking. NoFollow links are marked up in code with rel=”nofollow” and therefore do not pass PageRank.

NoFollow links are often used when the article/link is paid for, therefore the use of a backlink for monetisation purposes would be considered black hat SEO. It can also be used if the publisher’s content isn’t of large relevance to the linked site.