This is not a comprehensive answer, but just a couple examples of a natural backlink, as opposed to an artificial (paid for) backlink:
1. Someone likes an article on your website and shares it on Facebook. You got yourself a link to your site.
2. Someone is writing an article for their own blog and likes what you said on your blog. So they refer to your article, and they link to it.
#2 is the best kind of backlink, in my opinion, while sharing on Facebook may one day be seen by the search engines as artificial.