The inner ear (vestibular system) helps you maintain balance. The inner ear has a series of curved liquid filled canals that are also lined with sensitive hairs. As your head accelerates, the liquid sloshes around and the hairs pick up on the movement.

Being able to stablize your head during running lets you do a few thing:

* It probably makes it easier to continue tracking the prey. It probably makes it easier to see what the prey is doing (are they about to turn? are they looking somewhere? what's going on?)

* While running, if you can minimize any vertical movement, you can minimize energy consumption. Presumably even if your body/shoulders were displacing vertically while running, if you could maintain your head at a fixed vertical position with respect to the ground, you could save the energy put into moving the head against gravity. Obviously this advantage is heavily biomechanically and anatomically situational, and may not always be the case