Follow through is the termination part of an action. An example is in throwing a ball - the hand continues to move after the ball is released. In the movement of a complex object different parts of the object move at different times and different rates. For example, in walking, the hip leads, followed by the leg and then the foot. As the lead part stops, the lagging parts continue in motion.
Heavier parts lag farther and stop slower. An example is in the antennae of an insect - they will lag behind and them move quickly to indicate the lighter mass.
Overlapping means to start a second action before the first action has completely finished. This keeps the interest of the viewer, since there is no dead time between actions.
Here is a quote about overlapping from Walt Disney:
"It is not necessary for an animator to take a character to one point, complete that action completely, and then turn to the following action as if he had never given it a thought until after completing the first action. When a character knows what he is going to do he doesn't have to stop before each individual action and think to do it. He has it planned in advance in his mind."