All actions, with a few exceptions (such as the animation of a mechanical device), follow an arc or slightly circular path. This is especially true of the human figure and the action of animals. Arcs give animation a more natural action and better flow. Think of natural movements in the terms of a pendulum swinging. All arm movement, head turns and even eye movements are executed on an arcs.
Arcs are a major principle attached to the inbetweening process. Most actions follow an arc or curved path of action. The reason for this is that most actions work like a fulcrum or pendulum. For example, your arm swings from your shoulder. The length of your arm is constant and so as it swings back and forth, the path of action forms an arc.
Arcs add dimension to your movements, especially in the head. By tilting the head down slightly on a head turn, you can avoid a flat, linear movement.