It's basically when someone is aggressive but not direct about it. That is, they are passive. For example, making an insult that is disguised as a joke or faux concern is passive aggressive. Sulking is passive aggressive.
This is a good description of it, from www.counselling-directory.org.uk:
Passive aggressive behaviour takes many forms but can generally be described as a non-verbal aggression that manifests in negative behavior. It is where you are angry with someone but do not or cannot tell them. Instead of communicating honestly when you feel upset, annoyed, irritated or disappointed you may instead bottle the feelings up, shut off verbally, give angry looks, make obvious changes in behaviour, be obstructive, sulky or put up a stone wall. It may also involve indirectly resisting requests from others by evading or creating confusion around the issue. Not going along with things. It can either be covert (concealed and hidden) or overt (blatant and obvious).
A passive aggressive might not always show that they are angry or resentful. They might appear in agreement, polite, friendly, down-to-earth, kind and well-meaning. However, underneath there may be manipulation going on - hence the term "Passive-Aggressive".
Passive aggression is a destructive pattern of behaviour that can be seen as a form of emotional abuse in relationships that bites away at trust between people. It is a creation of negative energy in the ether which is clear to those involved and can create immense hurt and pain to all parties.
It happens when negative emotions and feelings build up and are then held in on a self-imposed need for either acceptance by another, dependence on others or to avoid even further arguments or conflict.
If some of this is sounding familiar don?t worry ? we all do some of the above from time to time. It doesn?t make us passive aggressive necessarily nor does it mean your partner is.
Passive aggression is when the behaviour is more persistent and repeats periodically, where there are ongoing patterns of negative attitudes and passive resistance in personal relationships or work situations.
Some examples of passive aggression might be:
Non-Communication when there is clearly something problematic to discuss
Avoiding/Ignoring when you are so angry that you feel you cannot speak calmly
Evading problems and issues, burying an angry head in the sand
Procrastinating intentionally putting off important tasks for less important ones
Obstructing deliberately stalling or preventing an event or process of change
Fear of Competition Avoiding situations where one party will be seen as better at something
Ambiguity Being cryptic, unclear, not fully engaging in conversations
Sulking Being silent, morose, sullen and resentful in order to get attention or sympathy.
Chronic Lateness A way to put you in control over others and their expectations
Chronic Forgetting Shows a blatant disrespect and disregard for others to punish in some way
Fear of Intimacy Often there can be trust issues with passive aggressive people and guarding against becoming too intimately involved or attached will be a way for them to feel in control of the relationship
Making Excuses Always coming up with reasons for not doing things
Victimisation Unable to look at their own part in a situation will turn the tables to become the victim and will behave like one
Self-Pity the poor me scenario
Blaming others for situations rather than being able to take responsibility for your own actions or being able to take an objective view of the situation as a whole.
Withholding usual behaviours or roles for example sex, cooking and cleaning or making cups of tea, running a bath etc. all to reinforce an already unclear message to the other party
Learned Helplessness where a person continually acts like they can?t help themselves ? deliberately doing a poor job of something for which they are often explicitly responsible
Passive aggression might be seen as a defence mechanism that people use to protect themselves. It might be automatic and might stem from early experiences. What they are protecting themselves from will be unique and individual to each person; although might include underlying feelings of rejection, fear, mistrust, insecurity and/or low self-esteem.
Patterns of unassertive and passive behavior may have been learnt in childhood as a coping strategy possibly as a response to parents who may have been too controlling or not allowing their child to express their thoughts and feelings freely. To cope, a child might adopt a passive-aggressive behavior pattern.

For example if a child was ridiculed, put-down or punished for openly expressing their feelings or disagreeing with their parents the child would learn to substitute open expression for passive resistance - agreeing with what mum or dad said in order to be a ?good child? or not speaking out honestly or at all. If there was a consistent pattern within the family of punishment or rejection for asserting themselves the child would learn to become highly skilled at passively rebelling. An example of a child rebelling might be around toilet training, withdrawing from family conversation, choosing subjects at school to please parents and then not working hard, around eating and mealtimes - all causing worry and upset to the parents who may have no idea their behaviour is a contributory cause to the problem.