This is aggression that is triggered by the dog’s instinct to hunt and kill. It can sometimes be focused on inappropriate targets such as other pets, domesticated animals, and even children.
Most aggressive behavior is motivated by a threat or challenge of some sort to territory, resources, status, self, and pack.
Predatory aggression is related to the instinct to hunt, chase, kill, dissect, and eat.
This instinct has been highly manipulated through domestication to help various breeds perform specialized tasks. Through the selection of suppressing and enhancing certain parts of the behavior, we have created dogs that show the micro-divisions of this instinct in different combinations (see a video explaining this here). For example, a border collie has a strong instinct to stalk and chase, but a lower instinct to bite. This allows the dog to perform the task of herding sheep without causing injury.
When the dog's predatory instinct is showing evidence that it will escalate to a damaging bite it is considered predatory aggression.
Learn more about predatory aggression and other forms of canine aggression here:
Classification of aggression types in dogs