What does 左 mean in Chinese?
The obvious answer is, of course, “left.”
But, come on, that’s boring. Let’s have some fun with this. And, as it turns out, “左” can be a pretty weighted word.
The most obvious secondary meaning is something along the lines of “left [wing]; revolutionary” in a usage pretty similar to the English usages of “left” and “right” in politics. A rather trendy term these days is 白左, the “white left”—a derogatory term for an affluent liberal that bandwagons on to various moral causes, and a rough equivalent to the English term “champagne socialist.”
In a very archaic sense, you might see it used to mean “assist,” especially in the sense of “assisting in governance.” These days, though, you’ll more likely see the word 佐 used for this purpose—左 was the ordinary usage, with 佐 introduced later for disambiguation purposes, much like 無 originally meant “to dance,” but later got its own character “舞” to disambiguate dance-無 from negative particle-無.
Apropos of this, you will sometimes see 左 (and 右) appended to a ministerial title in Imperial China, as in Chancellor of the Left and Chancellor of the Right (左丞相 and 右丞相). Generally, the Chancellor of the Left was the senior role, and Chancellor of the Right was either his deputy or headed some other role. During the Qin, for example, I believe that the Chancellor of the Left was in charge of civil affairs, while the Chancellor of the Right was in charge of military affairs, while the Chancellor of the Left during the Ming was “prime minister” and the Chancellor of the Right was his deputy. On the other hand, I believe during the Han, the Chancellor of the Right was paramount. It should be noted that this didn’t really have anything to do with 左 meaning “to assist [the emperor in governance],” it just dictated where they sat from the emperor’s perspective. This was actually copied to some extent by the Japanese, who for centuries had a Chancellor of the Realm (太政大臣), and then a Minister of the Left (左大臣) in charge of the overall running of the government with a Minister of the Right (右大臣) as his deputy.
Bizarrely enough, though, while 左 had the above meanings and usages, it also carries a meaning of “heterodox,” “strange,” or “improper” in certain contexts. 左道 has been used to indicate an unorthodox—even heretical—philosophy or even cult, and at times even carried connotations of what we might call “black magic.” Someone that is 左性 is pigheaded and stubborn, as in the idiom 牛心左性, “as stubborn as an ox.”
It can also mean “to conflict,” or “to fail to connect,” as in 相左 (“to conflict/’left’ with one another), for instance the idiom 意見相左 “to have views at odds with one another.”
It should be noted that “left” in a political sense here has no connection with “left” as in “heterodox” or “improper”; the latter is an old-attested usage, while the former is an import from the West just describing a political spectrum. I mean, using 左道 seems like such obvious wordplay for an anti-CCP propagandist from the 30s or whatever, so I’d be surprised if no one tried, but there’s no suggestion in the language that the political left is therefore unorthodox, just as there’s no suggestion that the Minister of the Left is a heterodox position.