民主 comes from Classical Chinese, where it originally meant “ruler” (of a people). It was repurposed I believe in the late Qing or early republican era to mean “democracy”.

民 means “people”, i.e. the population, the public. 主 means “host”, “owner”, or “master”. So while 民主 originally combined those to mean one who was the master of the people, it now is interpreted to mean the state of affairs where the people are the masters.

There is a related term, 民權, “popular sovereignty”, and also sometimes is translated to “democracy”, but it has a subtly different meaning than 民主. It comes from 民 (“people”, as before) and 權 (“power”, “right”, “authority”). Wiktionary doesn’t have the etymology, but I’m guessing it’s possibly a calque of Ancient Greek δημοκρατία (δῆμος, “people” + κράτος, “power”), possibly through one of the many European language words for democracy which derive from that, done during the late Imperial era, which is when many modern Chinese political terms were coined.