Alexa ranking is based on the amount of visits to your site by people using the alexa toolbar.

As I said this is mainly designed to help you rank higher for keywords your targeting. For example when somebody types "warez downloads" into google search. If you have many links to your site from other sites with the anchor text "warez downloads" your site will more than likely rank higher for that keyword than it would without all the backlinks.

The number of backlinks to a site also play a factor when google are working out pagerank and other things.