see also Follow URL
Nofollow links represent backlinks that will not pass link juice to the linked site, and search engines do not index them.
Nofollow links are backlinks created by third-party websites (most of the time) using a rel="nofollow" HTML tag to tell search engines to ignore that link when crawling is done.
Update: as of September 2019, Google seems to have changed the way it interprets “follow” and “nofollow” links. It has been suggested that Google may start taking into account “nofollow” links in some cases, regardless of the instructions coming from the website where the hyperlink is.
Usually, a backlink helps websites rank higher and be indexed faster because it passes on PageRank and trustworthiness. But by using a nofollow tag, a website actually communicates to crawlers and search engines not consider the link, so it won't pass link juice, PageRank, nor will it have any impact as a backlink for search engines.
If a website had multiple backlinks, but no sign of better ranking, a double check to see if the backlinks are nofollow is always a good idea. Here is a step-by-step guide to identifying a nofollow link: