The human body moves from its articulations such as the shoulders, knees, hips and elbows. Therefore, all limbs move by rotating on their pivot (articulation). When animating an arm going up or down, the hand will not reach its end point on a straight trajectory. It will follow an arc until it reaches its end point.
The motion of living things does not usually progress in straight lines. Most action follows the shape of an arc; for example, throwing a ball, swinging a bat, or nodding the head all result in arc-shaped motions.
The path of action is the direction that an action will follow. Think of a ball falling off a table and bouncing until it comes to a stop. The path of action helps map out the position of each drawing at each frame.