Continuity is important in cinematography. What is continuity? Contunity is consistency in composition and action direction.
Continuity in composition is maintaining all elements within a shot. For example, say you are shooting a scene in the dining room. The dining room has a fruit bowl with bananas, apples and grapes. In the first shot, you do a 2 shot with both subjects sitting across from each other and the fruit bowl in the middle of the table. The second shot you do a over the shoulder shot from subject 1 but for some reason you remove the fruit bowl to get a better view of subject 2. This violates continuity because no element should ever be removed. In doin so, it will distract the audience. Always ensure all elements in your shots match the next shots in a scene.
Continuity in subject action is very important. In subject action, a subject may move in a certain direction. See the video above posted by Martin Kools. The scene is taken from the movie Resevoir Dogs directed by Quentin Tarantino. Mr. Pink escapes a robbery, you can see he’s running from left to right in the shot. Observe cut after cut, you will notice the subject action direction continues to be moving left to right. By doing so, this ensures continuity. Now imagine if the shot started with Mr. Pink running from left to right. Cut, and the next shot he runs right to left. This will confuse the audience. Is he running backwards towards the cops? It is important to understand the direction of the subject of where he\she is going. Always, make sure the direction in motion is the same. Imagine you driving a car. If your coming East driving to West. You will always be driving towards West. A wide shot of a car driving will always start East(right) and end West(left) in the shot.
Continuity is important in cinematography. Understanding it helps you minimize distractions your audience may see and it helps better flow the story. There are many continuity rules in cinematography such as the 180 degree rule but I will be talking about that and more in another post.