In a general sense, link popularity is determined by the number and quality of websites that have linked to your website (often referred to as "backlinks"). The effects of link popularity are threefold: (1) links to your site give Web users ways to find your site while visiting other sites; (2) links to your site give search engine spiders (robots) trails to follow to find and index or re-index your site; (3) links to your site are essentially votes for your site in search engine ranking algorithms, but not all votes are counted equally.
When two sites are equally well optimized for search engine performance on any given keyword phrase, the search engine will generally rank the one with more link popularity above the other.
Google has a branded version of link popularity which they call PageRankTM. You can see a website's approximate PageRank by installing the Google Toolbar and visiting the page in question. PageRank is not simply derived by counting the number of links to a given site. A link from a site with lots of links or high-quality links pointing to it is worth more than a link from a site with few links or low-quality links pointing to it. You can read the Stanford University research paper that started all the hoopla about PageRankTMor read Larry Page's Stanford presentation, "PageRank: Bringing Order to the Web."
Using advanced search options, you can search specifically for websites which have linked to your website at all the major search engines.
