In its basic term, link popularity refers to the webmaster's technique of popularizing a specific website site (whether it be the main page of the site, or an internal page) with links from other pages on the internet.
This means, if your site is www.-------.com - you want to have links to www.-------.com coming from other pages and sites on the web. And if you receive a link from a site that is already indexed in the search engines (especially Google and Yahoo), this will get your site into the index even faster, and will enable it to rank higher for your search terms.
Getting links is crucial for online marketing today. Without getting those all-important links pointing to your site, a search engine has no way of knowing that your site is important enough to be ranked well. And on competitive keywords, you will not be able to rank at all without many high quality backlinks pointing to your site.