Link popularity is defined by the quality and quantity of inbound and outbound links of your web page.
Link popularity is used by search engines to determinate Ranking .eg: PageRank for Google.
What do we mean by quality?

Quality can be defined by the reputation of the websites that link to you, the context of the page defined in the title that link to you,the markup and text used in that link and few other factors detected by sophisticated text-matching techniques.
Interesting link ( Google) : Google technology

If we understand the importance of link quality, we must avoid a bad quality link. eg: Link farms, Low rank websites …
Conclusion : 10 Links of  quality will improve you Ranking, 1000 Links of low quality will result in a bad Ranking.