so just what is a martingale collar?

A martingale collar, also called a humane choke collar, is designed to tighten as needed, to provide the assurance that your dog cannot back out of it when used properly, but not to tighten so much as to cause injury. When loose it rests at a comfortable point on your dog's neck, and provides a convenient "handle" if you need to momentarily guide or restrain your dog.

When you need to restrain your dog, simply pull on the D-ring, with your hand or with your leash attached. This will tighten the collar sufficiently that your dog cannot escape. The collar will loosen again as soon as you release it. Please note this tightening is for control only; it is not meant to deliver a correction for training purposes.

Ideally, the slide rings of the collar will not touch each other when the collar is drawn up tight, ensuring that it cannot slip over your dog's ears at that point. This is especially important for sight hounds such as greyhounds, since their skulls tend to be narrow. On other breeds with larger heads this fit is not so critical, as long as the tightened length of the collar is smaller than the circumference of the dog's head.