when you link out to another website, that tells google that the site is probably kind of important. The more links you have, especially from important high traffic domains like bbc.com, the more likely it is that your site will rank for search terms. This is how it works by default.

Because lots of the web involves users being the content creators (comment sections and whatnot), Google created a "nofollow" tag that basically nullifies the above effect.

If you go to an article on bbc.com and post a comment with a link, I'm 99% certain without checking that it will have the nofollow link attached. It'd hurt bbc's own rankings as well as make their comments section unusable if not because it'd be spammed to hell by SEO people. So what you want is for your link to appear in the article or main body of content where they wont apply the nofollow tag usually (particularly if you pay for it), and google will think your site is hot shit.