I think you mean nofollow and dofollow. It is believed by some that adding no follow to links will keep the search engines from continuing on to the link. Some people think adding nofollow to external links will help their PR. I remember reading an article a few days ago proving that the search engines will follow the link anyway so it's really up to you what you want to believe.
Links with "nofollow" attribute don't pass PR juice while Dofollow links (without nofollow attribute) do pass.
If you insert your site link on a link page which has no follow attribute, it means your link will not get any profit. As the google crawler will not read no-follow attribute page. It is a code naming no follow tag in a website. you can check them via a tool. it will be seen as cut mark on a title which is hyperlinked.