backlinks are links that points to your website, incoming links. And they are so important because if you have many, Google will think that your site is important and rank it high.
Maybe these will help you http://en.wikipedia.org/wiki/Backlink Ohhh ... yeah and change the text size in the first post
They are basically links from other sites that link to yours. The more the links that point to your site, the higher your Google page rank and the higher you get in search results.