While multiple marriages and polygamy are definitely a thing in China, monogamy is considered by and large to be the norm.
The importance of marriage in China has a lot to do with Confucius. According to the Confuscian, the married couple serve as the primary unit in society, the most basic unit. This is a common notion in both western and eastern political philosophies.
A concubine is essentially a mistress, and has a much lower status than a wife. A man is allowed to take a concubine in Chinese society, however how many he is allowed to take was often regulated by his rank. An emperor would almost always have several royal concubines.
Sometimes a man would even take multiple wives, especially if he was someone who traveled a lot. It seems as though there have been some instances of women having multiple husbands, but this was viewed as disgusting (this is one common double standard).