This is often referred to as aggression that is related to a conflict in the dominant/submissive relationship between two dogs or human and a dog. It is also used interchangeably with the term “dominance aggression“.
When the context of the term is being used as a trait, such as: “This line of dogs is known to have high social aggression.”, or “This breed of dogs is usually selected for low levels of social aggression”, it is referring to the dogs’ tendency to show aggression for social reasons.
For example, some lines of Rottweilers and German Shepherds may growl at a stranger if that stranger or even certain family members try to give them a command. Some dogs will show aggression if someone tries to touch them. If the body language and history of the dog show that this aggression is not due to fear and is consistent with dominant posturing and rules of hierarchy than these dogs can be referred to as having high social aggression.
Certain dogs can have almost anything done to them and they will remain in submissive posturing and not show any aggression regarding the rules of hierarchy. This would be low social aggression.
Higher social aggression recognized as a trait can help predict how a dog may act in certain situations, so a trainer can be better prepared.