Link popularity is actually depends on how much sites link to your website this help yor rank higher for a certain search term. More links from other websites you will get, more higher you will rank. Link popularity works like this the search engines do not look at the content of your website to determine to if your site is relevant for a search term. They look at outside links that validate, by linking your site is relevant for that search.
Your site can gain link popularity when a high ranked site link to your site than less higher ranked sites linking to you. This means search engines look at how much important sites link to your site, this will give your site more link popularity.
The best long term method gain link popularity is to provide valuable content to your readers, this will help your site rank higher when readers will link to you because your site content is simply good. The most popular link building tool is getting links from yahoo and directories.