Prey drive encompasses all the behaviors which originate from the original instinct to hunt, kill, and dissect prey. More specifically this includes tracking, stalking, chasing, biting, holding, shaking, and dissecting (tearing apart). Different breeds were selectively bred to have stronger and weaker instincts within this spectrum, in different combinations, to best suit their task.
An important distinction of this drive is that there is no fear associated with prey drive. In pure prey drive a dog will not show signs of insecurity or signs of feeling threatened. Raised hair, growling, and deep sounding vocalizations/barks are never seen when a dog is in pure prey drive.
For the sake of discussing aggression, usually when dog training professionals state that a dog has "high prey drive" they are referring to the dog's instinct to chase moving objects, people, or animals and bite them. The aspects of prey drive that are related to the discovery of prey are generally lumped into the term hunt drive (which is not discussed in this article).
For a better idea of how prey drive relates to other aggressive drives read: Aggression Drives