What is it? An effort to avoid giving offense with respect to race, religion, creed, gender. Basically, being aware that there are people out there who aren't exactly like you, that their lives will have been different, and will respond differently than you to various things. At least, that's they what people assume it was "before it all went wrong".
But was it really? Nope. The phrase "politically correct" goes back to at least the eighteenth century, when it meant "to be in line with prevailing political opinion". To toe the party line, in other words. And that's the sense people use it in today. Like there's some sort of thought police or "politeness nazi" out there making sure you're only ever excessively courteous.
Was it ever really a thing? Yes and no. By 1970, it was briefly popular with the New Left, a sort of post-Marxist, left wing movement in the US and UK. In the 70s and 80s, however, it was used self-referentially and ironically1 by liberals, leftists, progressives, feminists, etc to guard against relying on orthodoxy. In other words, they were using it as a foil against what conservatives have been accusing them of ever since!
Did it ever go mad? Nope. Rather, there was a sea change regarding the political battleground of the US. Rather than being fought between races, classes, or even religious or political groups, the battleground in the US became divided between the ideologies of progressivism and orthodoxy, which in many ways transcend the other divisions. You find orthodox and progressive Christians2, African-Americans, and across classes. Now economists struggle to understand why poor white Christians have overturned the Republican party, making the Tea Party more than just an angry mob, despite that it advances the interests of the Koch brothers, aggressively libertarian, anti-poor billionaires.
This began in the 90s, perhaps coincidentally with the fall of the Communist bloc. Around this time, there also came into vogue an effort to get people to use kinder and more neutral language. "Challenged" instead of "retarded". "Disabled" instead of "handicapped" or "crippled". "African-American" instead of "black".
I'm not too certain about the right, but on the left, political correctness is usually approached apologetically. Like, "It's a good idea, right? I agree with it, but some people take it too far maybe?" This in spite of the fact that no one ever took it "too far". The only places where that ever happened were in parodies, like the Duckman episode, "Forbidden Fruit", or the Jeremy Piven vehicle, "PCU".
My recollection of the response on the right would be akin to "I'm gonna call a spade a spade! He's not 'challenged', he's a goddamn retard! And that guy's no more African than I am for all his funny shirts; he's black!" It is, at least in part, a way to act tough and sound tough, like you're standing up for freedom and stuff, but against whom? No one is actually enforcing anything.
Don't congratulate yourself for saying the hard truths. You're just an asshole.
Is PC a thing? Yes! It's called being polite. It's about recognizing that words actually do have power, and some are freighted with negative meaning thanks to historical realities. We say "developmentally disabled" because the former technical, medical term "retarded" went into common usage and became highly offensive. The exact same thing happened to the previous technical, medical term which was why "retarded", which means "slowed" or "halted", ie "developmentally disabled", was chosen to replace it. The previous term? "Idiot".
Political correctness never went mad. Political correctness was never a thing. The right acts like there's some sort of leftist conspiracy enforcing an orthodoxy, a Stalinist thought control experiment being enacted in our universities. Nothing could be further from the truth. "Political correctness" and "politically correct" were always used by the left to guard against that very kind of thing, and as usual, the right has stolen it (an orthodox mindset is almost constitutionally incapable of developing new ideas, it seems to me) and turned it against its former users.
All there ever was was an attempt to understand, an attempt to speak clearly, an attempt to be decent to our fellow human beings. How on earth is that a bad thing?
1 - proving the hippies were hipsters
2 - Though the right has fought long and hard to claim the title of Christian solely as their own, and to label all progressive "Christians" as "