Political correctness, as a movement, was a fairly effective widespread attempt to stifle freedom of speech
on university campuses by claiming that the speech hurt other people. Strangely enough, the movement was carried out primarily by baby boomers
, who had a few things to say about freedom in their own college days in the 60s.
Now the phrase is widely misused to promote political agendas by disparaging people who freely modify their own speech because they (personally) wish to avoid hurting people.
Your professor requiring you to use the term "developmentally disabled" rather than saying "retarded" would be an example of the former. But me calling you politically correct because you personally chose to use the term "developmentally disabled" -- and didn't require me to use it, too -- would be an example of the latter.