Link Popularity is a general form of indicating the total number of websites link to your site from different search engines, such as, Google, Yahoo, Bing, and etc.
Link popularity, also called inbound links or backlinks, is one of the most important factors used by search engines to determine your site rank on their search engines.
Generally speaking, the more inbound links a site has, the higher position the site achieves. (Of course, there are other factors associated with the site ranking.)
You probably notice that different engines show varied numbers of link popularity. This is because those search engines use different algorithms to filter inbound links to your site,
for example, Google only evaluates the relevant(related) inbound links to your site. Your actual inbound links are higher than they are shown in the Link Popularity tool.