I think people tend to currently overuse this term, making it an umbrella term which encapsulates other things like simply being polite or thoughtful or even diplomatic (these are actually different things). For me, being politically correct means to withhold/filter your true opinion/prime reaction for "political purposes"; like to prevent offending or insulting anyone based on how their beliefs (not just religious beliefs) differ from your own, in order to keep the 'conversation' going. The intention of this political correctness is to uphold relations, based on respect. Sometimes, I think people who are being "accused" of being politically correct are basically being accused of the possibility that this respect is feigned, thus resulting in them supposedly acting insincere.
Another currently overused term is "to be offended", which I think implies something different than being insulted or feeling hurt (yet it is used in these other two instances as well). I personally don't mind when someone uses this word, but like the phenomenon of political correctness (which is actually a positive term currently suffering a negative reputation), people are starting to get mocked for their outrage (ironically caused by what they perceive as a lack of political correctness). The downside to this is that people would simply give up either taking eachothers feelings into account or voice their own thoughts altogether. I think if people would experience the positive effect of political correctness, they would see it in a different light (also they would have less reason to feel offended).
Examples of a conversation (respectively) without and with political correctness:
When asked to make a donation for lower income households
- "Are there no prisons?"
- "Plenty of prisons..."
- "And the Union workhouses." demanded Scrooge. "Are they still in operation?"
- "Both very busy, sir..."
- "Those who are badly off must go there."
- "Many can't go there; and many would rather die."
- "If they would rather die," said Scrooge, "they had better do it, and decrease the surplus population."
During a Diversity Day excerise
"Okay, if I have to do this, based on stereotypes that are completely untrue, and that I do not agree with, you would maybe... not be... a very good driver."
[EDIT: Aside of being insulted or feeling hurt, there is also the phenomenon of indignation that can be placed next to feeling offended. However, I think this indignation precedes feelings of offense (instead of mainly being a similar term), so I'll just mention it here]