Political correctness is a term conjured up by SJWs in an attempt to hijack language and to take subjects and attitudes they don't like out of the debating sphere, or to make them taboo. Many of them will, as has been so ably demonstrated in this thread, divert attention from this agenda by claiming that it is all about not giving offence. In fact, many debates have been closed down in universities on the grounds that listeners might be harmed when they take offence at the views that might be propounded, and thus the subject cannot be debated at all in those places, at least by people that might disagree with the SJW view.
What starts off with saying 'you cannot describe someone as coloured' ends up as you cannot discuss race relations in any meaningful manner.
Being politically incorrect is to reject that attempt, and need not even involve using language that is impolite. On TSR, for instance, it is taboo to suggest that trans activists are wrong, no matter how politely you say it.
There is a similar attempt to cut off debate about Islam by labeling anyone who legitimately criticises the religion as an Islamophobe and conflating it with anti-Moslem abuse.
Those who seek to impose political correctness on us always deny it and are usually the sort of people I would label as regressive puritanical 'liberals' (with the word 'liberal' in inverted commas to show that they are in fact very illiberal despite what they think they are).