The core message of overlapping action is that not everything in an action—especially a character action—will move (or stop) at the same time. The biggest neglect of most inexperienced animators in either 2D or 3D animation is to put all the action of a character on the same keyframes. This is a major error.
To decide what is moving or what is the primary action and what is the secondary is something you have to quickly establish in your own mind. The primary action will dictate how the secondary action (or actions) goes. For example, a character with a cloak is running along with the cloak dragging behind him.