In addition to measuring your ability to pay, as in the United States, the scores serve as a measure of political compliance. Among the things that will hurt a citizen’s score are posting political opinions without prior permission, or posting information that the regime does not like, such as about the Tienanmen Square massacre that the government carried out to hold on to power, or the Shanghai stock market collapse.
It will hurt your score not only if you do these things, but if any of your friends do them. Imagine the social pressure against disobedience or dissent that this will create.
Anybody can check anyone else’s score online. Among other things, this lets people find out which of their friends may be hurting their scores.