We often consult with clients about the use of the nofollow tag. Sometimes our job is to identify whether or not a link from another website to our client's site is beneficial to our client's SEO, sometimes we offer advice on how our client should structure outgoing links on their own site.
The nofollow tag is one way that site owners tell search engines to NOT count a link to another web page as a “vote” in favor of that website.
Using nofollow can help site owners whose sites contain many links avoid problems with search engines believing they are participating in unacceptable SEO practices.
This infographic from searchengineland.com explains nofollow quite well.