an example would be telling your roomate that you wish you had been able to get more schoolwork done but it's hard for you to concentrate when there is a lot of noise (it's *passive* aggressive because what you are really *wanting* to say to roomate is: stop playing your music so loud!).
That would be an example of being polite.
I think a more accurate example would be if you ask someone to do something, and rather than them telling you they don't want to do it, they agree to do it but then take forever to do it, so essentially, it never gets done. Or they deliberately do it badly so you'll never ask them again. They don't have the guts to tell you 'no'...but their actions are conveying their thoughts & feelings in a passive-aggressive way.
It allows them to get out of doing something they don't want to do, without being confrontational about it.
A perfect example would be the old Bill Cosby story about his wife asking him to make the kids breakfast. He doesn't want to, but she is in a bad mood so he doesn't dare tell her that. Instead, he goes downstairs and feeds them all chocolate cake. When she finds out and freaks out, his reasoning behind it was that cake contains eggs, milk, flour...all the things in pancakes...it's nutritious...and then adds that they wanted the chocolate cake...they asked for it (blaming the kids for his screw up). So she never asks him to make breakfast again, because she doesn't want him to screw it up again.