The nofollow tag is a way publishers can tell search engines not to count some of their links to other pages as “votes” in favor of that content. Why would publishers need to block such votes? Doing so can help them avoid problems with search engines believing they are selling influence or are somehow involved in schemes deemed as unacceptable SEO practices.
Search Engine Land created an infographic which can be found below. It explains more about the nofollow tag, including when and how to use it.