Regarding the Chinese, polygamy basically came about as a way of ensuring there would be a heir in the line of succession. For instance, if your first wife repeatedly failed to conceive, you might draw the conclusion that she was barren, and seek another, younger wife who could provide you with an heir. However, since marriages were often politically-charged, to divorce your barren first wife would be seen as an insult to her relatives. The solution is therefore to have a second wife, seen as a junior to your first wife, and "lower ranked" in the family hierarchy.

Another reason is because your first wife consistently gives birth to daughters. Since daughters lose the family surname when married out and do not preserve the direct lineage of their father, they cannot carry on the family legacy. In this case, it is also cause for a man to look for a second wife.

Polygamy was not common with the general populace of China. Instead, it was something that was mostly confined to wealthier, noble families, who could afford to have multiple wives. It was especially common in the imperial household. Emperors, apart from having an official "Empress", would also have multiple concubines.

Polygamy was also sometimes done to enlarge a family. The Chinese knew that a direct line of male succession did not always ensure the continuation of a family legacy. To that end, noble Chinese families, and especially imperial dynasties, actively sought to create multiple branches of their family via polygamy.

This is related to the Chinese imperial punishment policy known as "guilty until the ninth generation/kin/clan", or zhu lian jiu zu (株连九族). An especially serious form of punishment, often used as a means of punishing high treason, this form of punishment ensured not only the offender would be put to death, but also all relatives to the ninth generation. This meant all surviving grandparents, parents, siblings, uncles and aunts, all your descendants including children, and anyone living in the same household regardless of relation, such as servants. This was seen as an effective means of purging any possible retaliation by surviving kin, and may have been due to the noble/imperial policy of expanding your family through as many branches as possible. While rarely used for obvious reasons (except by certain tyrants in history), it served as an effective threat to force people into compliance.

On an interesting but somewhat unrelated side note, to be guilty till the "tenth generation" would also include all your friends and any students you may have had.

Incidentally, the CPC/CCP banned polygamy when they came to power, and it continues to be illegal in modern China.

References:

• Davis, Edward (2005). Encyclopedia of Contemporary Chinese Culture. Taylor & Francis. pp. 897–899.

• The history and evolution of '株连九族' (2016) by Xinhua, or "株连九族”的历史演进 – 新华网"

• Rubie Sharon Watson, Patricia Buckley Ebrey, Joint Committee on Chinese Studies (U.S.) (1991). Marriage and inequality in Chinese society. University of California Press. p. 225.