Anticipation can be two things. Relating to movement it means the delay ,wind up or store of power before a movement. this happens in everyday life even if you watch some in a city stand and then start to walk there is a weight /momentum shift backwards before it goes forward to create a direction of movement. ie. a frisbee throw there is a large back swing before a quick snappy forward release, notice the arm continues to move after it has been thrown. this is an example of over lapping action but we'll come onto that later.
or this example of anticipation in the framing of a shot. this particular example is from Luxo Jr. (Short by Pixar) where the luxo lamp looks out of frame ANTICIPATING something happening off frame or something about to enter the frame.