When the main body of the character stops all other parts continue to catch up to the main mass of the character, such as arms, long hair, clothing, coat tails or a dress, floppy ears or a long tail (these follow the path of action). Nothing stops all at once. This is follow through. Overlapping action is when the character changes direction while his clothes or hair continues forward. The character is going in a new direction, to be followed, a number of frames later, by his clothes in the new direction. "DRAG," in animation, for example, would be when Goofy starts to run, but his head, ears, upper body, and clothes do not keep up with his legs. In features, this type of action is done more subtly. Example: When Snow White starts to dance, her dress does not begin to move with her immediately but catches up a few frames later. Long hair and animal tail will also be handled in the same manner. Timing becomes critical to the effectiveness of drag and the overlapping action.
These are used in combination with each other. Follow through is used for parts of the character like hair, clothing, a dress, ears. These are all things that usually hang on a character. The primary action comes from the character’s body, then when the character comes to a stop, something like the long ears on a dog continue to move, then settle to a stop. Nothing on a character should ever come to a stop at the same time, if they did, the character would seem to suddenly freeze. There are lots of different ways to make this work.
Overlapping action is similar but can also be applied to primary actions like a character walking. The characters arms swinging back and forth are good place for some overlapping action. You could keep the arms stiff but by applying overlapping action, it gives a much more interesting and natural movement. The main idea behind overlapping action is the principle of successive breaking of joints; the “seaweed action” fully explained in my other book Animation: The Basic Principles.
Timing on follow through and overlapping actions are very important. If it’s too slow, it becomes obvious and makes the primary action look awkward, too fast and you can’t quite see it.