My grandson asked that question last night as we sat together waiting to ambush some of the bristly beasts that had been visiting a feeder.

I told him that there was not a whole lot of agreement on the subject, but, in general it is a combination of a few things:
Destroying something critical in the Central Nervous System
Destroying a crucial organ, like heart or the lungs
Rapid blood loss, causing the animal to go into shock
Hydrostatic shock produced by the bullet as it passes through the tissue and interrupts the function of critical organs with pressure waves

I told him that the reason we shoot pigs in the ear is to get into the brain cavity and shut the whole CNS down, and that I thought that was the quickest, one-shot way of taking them out.

Have any of you got some knowledge to add?

I’m glad you have a Grandson that asks the question, these days the Internet gets a lot more hits than Grandpas for life’s little mysteries...

Only thing I’d add is velocity and energy - that’s always a fun talk

In regards to hunting (versus chemical or disease kills), the goal is a quick lack of oxygen to the functioning brain.

This can be accomplished by destroying the brain or depriving the brain of oxygen.
Lack of oxygen to the brain can be accomplished by disruption of the pulmonary system
Pulmonary system can be disrupted by airway disruption or lung disruption
Airways can be disrupted by destruction or blockage
Lungs may be disrupted by destruction, blockage (lungs filling with blood), or cessation of movement due to CNS damage.

Lack of oxygen to the brain can be accomplished by disrupting the cardio system
Cardio system can be disrupted by destroying the heart (cessation of pumping), by destroying vessels that carry the blood causing there to be a lack of blood in the system (exsanguination), or by cessation of movement due to CNS damage.

Most kills are produced by direct physical damage of projectiles, but also by indirect physical damage by hydraulic shock or hydrostatic shock that result in the damages necessary to cause the disruptions above.

Hydraulic shock is the damage produced by the direct shock wave produced by the bullet and follows the bullet tract. In many cases, it can be traced out as being cone-shaped (cone of percussion), though may appear to be tubular. This is generally where you see the temporary wound cavity damages.

Hydrostatic shock is the remote wounding caused by pressure waves and is usually associated with higher velocity projectile >2600/2700 fps. Where it does its damage is in the burst capillaries of the CNS, particularly of the brain stem or brain, essentially stroking out the animal on a grand scale resulting in brain damage and/or cessation of the ability to send signals to the body's systems. For example, a bullet to the chest that misses the spine by a wide margin but still drops the hog in place may be a hydrostatic kill.

Hogs that are shot and run have not suffered significant CNS damage, directly or indirectly.

Thanks, guys. We had been reloading earlier in the day and I showed him some of the work I had done with the chronograph while developing loads for the new Ruger PCC 9 carbine (which he now feels is his!), and then from the velocities, computing the energy of each projectile at that velocity. He let all the information turn over in his brain for a few hours and then came up with the "how does it work" question. It appears, based on what you guys have written, that I was close, but not complete in the correctness of my answer. DNS I'll lay your whole package on him so that he understands the physiology of GSW's a bit better. He's a good kid, with an inquiring mind, and I run fast to keep up with his barrage of questions. . .

Ya, makes ya stop & think. Just one of lifes little mystries