Overlapping and Follow through its one, of the twelve principles of animation, created by ex-Disney animators Frank Thomas and Ollie Johnston. The main purpose of these principles was to produce an illusion that cartoon characters adhered to the basic laws of physics, but they also dealt with more abstract issues, such as emotional timing and character appeal.
Follow-through and overlapping action are two very closely related topics that generally accomplish the same goal of realistic motion. Follow-through is the idea that certain appendages and body parts might continue to move even after a motion is completed. So if a character with a scarf is running, then they stop suddenly, the scarf will fly forward past the body, then fall back where the character stopped. If a car stops moving, the antenna on top will keep moving for a second. If a cat turns suddenly, their tail might whip around.
Overlapping action is the idea that different parts of a body will move at different rates. So if you walk, your arms will move at a different speed than your head. Both overlapping action and follow-through are ways to provide convincing motion to animation.