In terms of psychology, at least, aggression is defined as any act that is meant to bring harm to another person--to make them suffer or to in some way damage them. This means that aggression can take many forms.
For example, there can be direct physical aggression. Punching someone is meant to hurt them and is therefore aggression. Stealing from someone's home could be aggressive as the loss of valuable possessions would cause emotional pain to the person. Finally, words can be aggressive. We know that words have the power to hurt.
Additionally, the link below give detailed discussions of aggression and the causes of aggression.
The Encyclopedia of Psychology defines aggression as "any act that is intended to cause pain, suffering, or damage to another person." It is a sequence of behaviors with the object of causing injury to a member of one's species. This is in contrast with the concepts of predatory and defensive behaviors and of assertiveness. Predatory and defensive behaviors accur when a human being wards off (defensive) an attacking (predatory) dog to defend himself. On the other hand, being assertive - which is sometimes used as synonymous to being aggressive - does not have that element of intent to harm and should not be confused with aggression in this case.
The meaning of agression somewhat varies from author to author depending on the school on which they tend to lean on. Some psychologists consider aggression as a consequence of completely inherent factors, mostly the instinct to survive. Others see aggression as externally-stimulated where a defined stimuli (frustration) creates an aggressive behavior; and still others consider aggression as a learned behavior. Either way, in normal psychology, the behavior is always intentional and is directed to another person.