A nofollow link is a link that includes a rel="nofollow" attribute, which tells Google not to pass ranking credit (link equity) through that link. A normal link — often called "dofollow" — is the default and does pass authority to the page it points to.
The purpose is to let you link to something without endorsing it in Google's eyes. If a local news site links to your business in an editorial article, that is a normal endorsing link. But if you pay for a placement, or a random commenter drops a link in your blog comments, you would not want to vouch for those — nofollow is how you say so.
