Back Links are links from other sites back to your own. For example I have a back-link from the BBC website this is a link from their site to a personal blog of mine. It was a blog post I wrote about one of their programmes.
Sometimes these back-links carry authority too.
Let me go back a step, for example with the BBC they can put a link on their site and it would be a ‘no-follow’ link. This means that people visiting the site would see the link and click on it to go through to my website and I would gain the traffic from this. The no-follow part means that Google would not see this link to my site.
Then there is a ‘do follow’ link, this means that people would see the link and click through (gaining traffic to my site) and because it is a ‘do follow link’ some of the authority from that site would come through to my site and the more authority on my site the better my ranking would be in search engines. (Simple?)
This is why some people employ the use of a ‘guest poster’ or a ‘link builder’ to help gain back-links and authority for their sites.