Passive-aggressive behavior is the indirect expression of hostility, such as through procrastination, sarcasm, stubbornness, sullenness, or deliberate or repeated failure to accomplish requested tasks for which one is (often explicitly) responsible.
For research purposes, the Diagnostic and Statistical Manual of Mental Disorders (DSM) revision IV describes passive-aggressive personality disorder as a "pervasive pattern of negativistic attitudes and passive resistance to demands for adequate performance in social and occupational situations".
There are three people in my life whom I recall having heard label other people "passive-aggressive." Interestingly, these three people treated others harshly. I think their harsh treatment of other people temporarily brought out behavior typical of those with genuine passive-aggressive personality disorders.
The first person I heard lecture about the evils of "being passive-aggressive" was a high school music teacher who was very hard and critical. Multiple kids refused to continue in school music classes specifically due to his personality. He was so energetic when yelling at students that he once broke his directing baton on the edge of his stand. Since I sat near the front, it flew my way, and I still have the baton fragment (rather an odd souvenir from high school). I suspect he ran into a lot of people who responded in quietly hostile ways because he seemed so mean. That seems more probable than large numbers of people with passive-aggressive personality disorders being concentrated in his vicinity by random chance.
The other two people are my father and my husband's older brother. I have seen both of them bring out passive-aggressive behavior in my husband, ordinarily a well-meaning, helpful person in nearly all his actions and thoughts. Interestingly, my husband is an introvert, and if I'm reading it right, a recent study found that introverts are more likely to exhibit passive-aggressive behavior. My personal experience (and, yes, I'm introverted, too) is that it is not worth the hassle of open conflict all the time with domineering people, but that doesn't mean that I'm going to happily submit to everything they say or want me to do. Sometimes a little sullenness is justified when it's impossible to prevail via open conflict, particularly when dealing with "authority figures" who think they should always win because of pride and/or their position of authority. Does this work for me? It certainly feels healthier mentally than being a complete doormat or embroiled in frequent fights.
When encountering quiet resistance from a subordinate (or someone we treat as a subordinate), I think it is more productive to ask one's self, "Why is this person behaving hostilely towards me?" than to think, "Oh, that person is just being passive-aggressive." Odds are that, rather than facing someone with a personality disorder, we might be provoking the hostile response with unkind behavior.