Alright, there are two main values that are used in the rel attribute for the anchor tag: nofollow and external.
nofollow will tell search engines that this link is not trustworthy. So what means is that Google will not give any credit to this link for your site. It’s not going to pass any PR to your site but it might still bring you some traffic. Even if it shows as a backlink to your site, it’s of no value, remember that.
Here’s the URL that talks about it from Google Team: