An Arc is the most natural movement in the real world. Animation would look unnatural with out this motion used with everything. When you turn to look from side to side the movement is not straight back and forth, the face dips down in front and rises on the sides.

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.

Since in animation, we can plot any arc paths, and structures will follow; we can defy reality, but they have to feel 'right' and comfortable to look at in motion.

In short, strength of internal force (embodied in character's structure and mass), interacting with gravity and other external forces determine the curvature, distance, and path of the arc.