Quality Score are variables used by Google, Yahoo, Bing, Yandex, Baidu, Naver, and other search engines that will both influence a website rank (called Quality Index), and cost per click (CPC) of ads.
Purpose behind Quality Score
In order to determine the order in which ads are listed, each ad has the following formula run against it for: bid * Quality Score. Ads are then listed in descending order based on the result of that equation. The exact weight of Quality Score versus bid and will not been revealed by any major search engines, and each company reserves the right to continuosly adjust their ranking methodologies.