Confucianism was a massively important factor in delineating between being Chinese and not. Rather than using ethnicity or language, the degree of cultural assimilation (開化) was quite important. As a result, those who were less assimilated (未開化) would be frowned upon or even considered barbarians. The Qin dukedom was one early example. Many non-Huaxia peoples (such as the Xiongnu and Baiyue) were incorporated into Zhonghua and has helped shaped the modern Han identity, much like the many Gothic tribes along Rome's borders

During the Liao Dynasty, they even differentiated between "Cooked Jurchens" (熟女真) and "Raw Jurchens" (生女真) based on how urbanized and assimilated the various tribes were. The Raw Jurchens were descendants of the Jin Dynasty (金朝 1115 to 1234) that fought against the Mongols, whereas the Cooked Jurchens established the Later Jin before renaming themselves as the Manchurians (滿人) and their dynasty as the Qing (清朝). The Qing Emperors managed to hold together their empire with an interesting concept of identity that appealed to their four major population groups (Manchus, Mongols, Tibetans, and Chinese). They were simultaneously khans of the Manchus, husbands to Mongol princesses directly descended from Genghis Khan, Buddhist lamas worthy of Tibetan loyalty, and Confucian sages who held the Mandate of Heaven and were therefore qualified to rule Zhonghua and the overwhelming Han majority

The Mandate of Heaven (天命) sounds like a "divine right to rule" kind of concept. But at its core, it actually depends heavily on the will of the people (民意). A Chinese phrase from Xunzi (荀子) in the Record of Rites (禮記) that captures this concept states, "The ruler is a boat, and the people are water. The water can carry or sink a boat."

君者舟也

庶人者水也

水則戴舟

亦可覆舟

Rather than a democracy-style will of the people, the concept meant that the people would rise up against corrupt and incompetent rule, but follow strong rule. Of course, this meant that sometimes a violent warlord would gather the right mix of talent and take over Zhonghua (as was the case for the Ming Dynasty), but then following emperors were responsible for maintaining the will of the people. This usually meant timely disaster relief, defending the borders, maintaining peace and prosperity, etc.

The concept of the "mandate of heaven" (天命) was, in reality, mostly applied in retrospect by victors and historians, rather than commonly invoked in ancient Chinese politics. It wasn't as if rebelling warlords chose their moment to rise up based on whether or not they believed that the ruling power had suddenly lost 天命, but rather a way for them to justify their victory and validate their rule after being successful-- or conversely it was a way for historians and emperors to justify or explain crushing or having crushed an unsuccessful rebellion and thereby lend further validity to their continued rule. 天命 as a concept wasn't a drive for sustainability or rebellion; these things happened for the same sorts of reasons as they did elsewhere and were only interpreted differently.

The re-interpretation and uses of the Mandate of Heaven for legitimacy during the Galdan wars (1690-1697) might be interesting here.

Before and after each the campaigns, the emperor (Qing) imitated the sacrifices to Heaven and Earth made by the (Ming) Yongle emperor: this stressed the continued use of the Mandate of Heaven by the Qing dynasty and therefore continuity with the Ming dynasty. By contrast, Galdan's legitimacy was based on an alternative Buddhist concept.

Secondly, the Qing worked hard to demonstrate this continuity. The 'fanglue', the officially commissioned military campaign history, was an innovation of the Qing, though it had precedents in the shorter, more personal, and unofficial accounts of NW campaigns of the Yongle Emperor. In this account, the dates of the fourth expedition under the Kangxi emperor was altered so that the expedition was not revealed to be useless (Galdan having already died in suspicious circumstances). Further, the emperor was supposed to have forseen Galdan's death as a suicide. This emphasised the emperor's omnipotence.

The Mandate of Heaven, in this example, served as a legitimising tactic both at the time, during a war against another powerful movement, and in retrospect. It tied the Qing to the Ming.

I've just re-read your question and noticed the word 'ancient'. Hope this is useful anyway though! Or at least interesting.

Confucianism is a system which created a structural hierarchy in society, there was very specific order. It was all laid out in his Analects. In addition, the Mandate of Heaven was claimed to show authority because it would be believed that the rulers were ordained by God.

Two further points—it's interesting to note the Mandate of Heaven also led to the downfall of some governments in ancient China (it's easy to think the rulers have lost it when things start going poorly); and many also appealed to the Han ethnic background, claiming a "right-to-rule" based on their connection to the major ethnic group that we think of as "Chinese."

They were basically systems of societal order, like the Constitution, the Rule of Law, and Meritocracy in the United States.