What is it? It means that what’s happening on screen – the action – makes narrative sense in combination with the camera movement, the set, and the lighting.
Motivated camera movement is any camera movement makes sense based on the story. Zooming denotes special emphasis; dolly and tracking shots follow the action; focus and depth of field are based on what is important in the narrative at that moment, i.e. what you want the view to follow and focus on.
The beginning and end point of dolly and tracking shots should be motivated, i.e. dollying or tracking should be integral to the action and the narrative – should begin for a reason that is narrative-dependent, and should end because the narrative reaches a particular point of emphasis.
Motivated lighting means that the scene is lit based on the logic of what appears to be a light source in the scene, whether or not it is actually the light source in the narrative.
It helps with both lighting and camera movement to plan where the shot will end before planning where it will begin. The shot should settle at a point that allows for ease of continuity with the next shot/scene, especially if the next clip is static. End your camera movement on a static note if your next shot is static.
Motivated camera movement means incorporating camera movement into the plot. Zoom in on an important element; or reveal, through camera movement, something else in the scene that moves the plot along. The camera captures the action and camera movement, in combination with dialogue and acting, takes your story into the next scene.