An example: Laura and Charles are discussing dinner plans over the phone. Laura wants to meet friends at a restaurant later in the evening. Charles wants to stay home, but does not say anything knowing that Laura will not listen but will instead respond with anger and intimidation, instead mumbling an "ok." Then, when Laura is off the phone, Charles decides to stay home but does not tell Laura. She arrives at the restaurant with her friends but Charles is not there.
In some instances there may be some sort of covering behavior; in our example that would consist of Charles concocting some sort of excuse for staying home (I felt sick) and not communicating the change in plans (I called but your cell phone wouldn't work). In other instances, passive aggressiveness is more overt, such as locking yourself in the bathroom in the middle of a fight.
Passive-aggressive behavior usually has roots in communication difficulties, or in relationships that lack effective power sharing.
Passive aggressive behavior gains its power from reduction of expected behaviour rather than the addition of assertive behaviour. Consequently, often it comes in the form of ultimata ("I won't come out of the bathroom until..."), and therefore it often fails if the intended victim does not require the missing expected behaviour as they will simply call you on the ultimata ("Ok, stay in the bathroom. I'm going out for drinks."). However, this will make the aggressor even more infuriated, possibly enough to overreact actively aggressively.
See GoodBye as an example of a popular passive aggressive strategy in OnlineCommunity.