Noah's Arcs.
Arcs are important to life like movement, this is due to the rotation of joints in a person or an animal or the rotation of a gear in a machine. The result of this pattern is an arcing path of action that an animator may notice and thus latch on to.
Thus arcs are a principle of animation due to their addition to the quality of an animation. An animator should focus on key points where arc like movement would occur, like the full extension of a leg as a person walks, or someone waving their arm.

See why the arch of your foot is so important? It allows you to move normal. (That is a joke and i am flat footed myself, homies)
Arc like movement however may not be obvious is nature, but more subtle. Like an arch of a brow in confusion, or the twist of the mouth in bemusement. The arc principles are important for bodily motions, and that includes the facial expressions of a character.

Something as simple as the turn of the head is indeed an arc, and thus the arc principle is a massive part of the animation of movement.