Can anyone explain what NP-hard means?

So I’ve just discovered that something I do every month is known to have NP-hard complexity (Nurse scheduling). Any one care to have a go explaining what that means? And preferably do a better job than Wikipedia page.
I’m guessing (from experience) that it means there’s no simple way of getting to a correct answer but that once you have an answer it’s easy to tell if it’s correct (by the number of angry people trying to kill me)...