Slow in and Slow out is the movement of the human body/animal or intimate object which is made more realistic by the manipulation of time on the moving parts. What this means is that the time manipulation is used to show the speed differences between the limbs/parts of the animal/human or object that are moving. A perfect example of this is the arms and legs of a human when walking the legs and the arm will both move at different speeds from each other so the legs move slower then the arms.
A perfect example of this is the first episode of Medabots:
Watch the clip from 2:43 to 3:00 minuets. The reason why this is a good example is due to the fact that the during this given time frame several different speeds are used by the character and the object he is holding to create a feel of realism with how the character interacts with the environment and the object the character is holding. This is one of the most important principles due to the fact that it allows each of the characters to have their own style of movement that suits the characters own personality and appearance. The main reason why I chose this clip is because the speeds used within this clip each define a key moment within it, for example the fastest speed is used to define that the character is panicking and the slowest speed is used to display the rippling of the water.