“Nofollow” provides a way for webmasters to tell search engines “Don’t follow links on this page” or “Don’t follow this specific link.”

Originally, the nofollow attribute appeared in the page-level meta tag, and instructed search engines not to follow (i.e., crawl) any outgoing links on the page. For example:

<meta name=”robots” content=”nofollow” />
Before nofollow was used on individual links, preventing robots from following individual links on a page required a great deal of effort (for example, redirecting the link to a URL blocked in robots.txt). That’s why the nofollow attribute value of the rel attribute was created. This gives webmasters more granular control: instead of telling search engines and bots not to follow any links on the page, it lets you easily instruct robots not to crawl a specific link. For example:

<a href=”signin.php” rel=”nofollow”>sign in</a>
How does Google handle nofollowed links?
In general, we don’t follow them. This means that Google does not transfer PageRank or anchor text across these links. Essentially, using nofollow causes us to drop the target links from our overall graph of the web. However, the target pages may still appear in our index if other sites link to them without using nofollow, or if the URLs are submitted to Google in a Sitemap. Also, it’s important to note that other search engines may handle nofollow in slightly different ways.

What are Google’s policies and some specific examples of nofollow usage?
Here are some cases in which you might want to consider using nofollow:

Untrusted content: If you can’t or don’t want to vouch for the content of pages you link to from your site — for example, untrusted user comments or guestbook entries — you should nofollow those links. This can discourage spammers from targeting your site, and will help keep your site from inadvertently passing PageRank to bad neighborhoods on the web. In particular, comment spammers may decide not to target a specific content management system or blog service if they can see that untrusted links in that service are nofollowed. If you want to recognize and reward trustworthy contributors, you could decide to automatically or manually remove the nofollow attribute on links posted by members or users who have consistently made high-quality contributions over time.
Paid links: A site’s ranking in Google search results is partly based on analysis of those sites that link to it. In order to prevent paid links from influencing search results and negatively impacting users, we urge webmasters use nofollow on such links. Search engine guidelines require machine-readable disclosure of paid links in the same way that consumers online and offline appreciate disclosure of paid relationships (for example, a full-page newspaper ad may be headed by the word “Advertisement”). More information on Google’s stance on paid links.
Crawl prioritization: Search engine robots can’t sign in or register as a member on your forum, so there’s no reason to invite Googlebot to follow “register here” or “sign in” links. Using nofollow on these links enables Googlebot to crawl other pages you’d prefer to see in Google’s index. However, a solid information architecture — intuitive navigation, user- and search-engine-friendly URLs, and so on — is likely to be a far more productive use of resources than focusing on crawl prioritization via nofollowed links.

https://support.google.com/webmasters/answer/96569?hl=en