This is given in the HTML page or the Robot.txt of the website, in order to direct the search engines to follow that particular web page.
the opposite is a nofollow link. Which, obviously, means that the search engine will not follow the link and it will not provide a backlink. Basically you want dofollow instead of nofollow if yo can. But nofollow can be useful for generating traffic.
No one is 100% sure about Nofollow links because in webmaster tool are links are shown whether they are dofollow or nofollow.
All links are considered as links, except that when you add comments on dofollow blogs, the comments with your url have the added advantage of search engine spiders following the link to index your blog.
always making reply to post on forums will always provide do follow, and act as backlink to your site