What it "really" means is the choice or control of language according to some political ideology -- usually liberal-left ideas. Different people take this to be a good thing or a bad thing, though. Mostly according to their political ideology or the supposed extent of the control. So the term emphasises different behaviours when used by different people, and in my experience is commonly used to describe pretty much anything from discouraging the use of expletives, to discouraging the expression of views opposing immigration.
Disclaimer: I am broadly sympathetic to the project taking prejudiced language out of the norm of public discourse, although I'm unsympathetic to the notion that any word must never be used under any circumstances, and also to the notion that straying from correct expression is necessarily bad. This will no doubt affect how I represent the use of the term!
Of course since it's all about political discourse it is frequently mis-used, both accidentally and tactically. People do not always assess with precision the difference between attempting to control expression, vs. merely disagreeing with or disapproving of the views expressed! This is so common that I think one could make a case for "political correctness" having lost most of any precise meaning it ever had.
You can look at a lot of examples of it being used in slightly different ways in etymological sources or the Wikipedia article. It "really means" all of those things that it was used to mean, and understood by the person who heard it used. What links them is the notion that there are certain words or phrases that should or should not be used according to whether one approves of the concepts behind those words.
Now, if one believes that all of the excluded words are unfair and prejudiced, then to be "politically correct" is to use a fair, neutral, unprejudiced vocabulary. That does not imply actually being neutral or even being fair and unprejudiced. Some consider it a necessary but insufficient condition. The term is normally used somewhat derisively, so normally is not intended to mean "neutral" at all, it means "supporting a particular ideology by controlling the use of language".
I think the term is most commonly used to express hostility towards the idea of language being "good" / "bad", "allowed" / "not allowed", with the implication being that the "politically correct" vocabulary is not fair or neutral. In such cases the term "political correctness gone mad" is commonplace, to the point of being a cliche here in the UK, and often to describe some invented or easily-solved outrage. Many people feel about political correctness approximately the same way they feel about health and safety (another idea that gets attention primarily when it has "gone mad"). They feel that to criticise the use of particular words is by definition an unreasonable interference with common sense and personal liberty.
However, since that's the same common sense that used racial slurs commonly in everyday conversation 40 years ago, and since in any case common sense dictates avoiding certain words in certain contexts for a variety of reasons, I think one can reasonably question the universality of common sense ;-) There is of course a response to that hostile usage, where people use the term more positively, trying to counter the notion that "political correctness" is inherently nefarious.
During the 70s and 80s, though, it was applied self-mockingly by those who supported an attempt at changing the vocabulary of public political discourse, since they were aware that the analysis and moderation they were trying to apply to their own use of language and that of other people, could be compared with the censorship of ideas during the Cultural Revolution in China. The reference is to the idea that during the Cultural Revolution the term was used (not originally in English, I assume) for a body of ideas that were "politically correct", i.e. in accordance with ideology. Being "politically incorrect" under Maoism could be very dangerous. AFAIK the modern uses can be traced back to this description of Maoism.
So, "political correctness" can mean rolling your eyes when someone uses the n-word, or it can mean executing political dissidents. Naturally that makes it something of a weapon in the hands of someone who wants to use the n-word without anybody rolling their eyes. But it also describes a genuine danger for those who want to suggest that a less-commonly-reviled word than that is inappropriate to use. The risk is that of interfering with usage that actually is more-or-less innocent.
For example English has in it racial insults such as "welshing on a bet", "Dutch courage", that the people using them genuinely don't intend as racial slurs, although no doubt they can puzzle out the origins of terms once they put their minds to it. More mildly, the use of the word "lame" to mean "bad in some way" is a slur on anyone with a limp even though I'm pretty sure it's just an analogy based on the fact that lameness by definition is walking badly. The problem is the choice of physical disability as the canonical representation of "being bad". These terms are politically incorrect, and sometimes are actually insulting. But one might resent interference with the language on the basis of what one sees solely as irrelevant etymology, especially if you feel like you've been accused of being a racist just because you don't know what something originally meant, or because you see two meanings as conceptually unrelated even though the etymology is clearly via an intentional prejudice against a particular group. So even when the term "political correctness" is used in a hostile way to mean "inappropriate authoritarianism over language", it's not always disingenuous.
I think the example from 1793 is a use of the term literally: that one or the other term was accurate in terms of politics, and the other was inaccurate. You'd think that's unrelated to the modern use, which is far more specific than the literal meaning and not even entirely consistent with it. It's not what the term really means any more than "terrible" really means "inspiring terror", but naturally all words can carry shades of their former meanings, as idioms do of their literal meanings.