Movement is all about moving the viewer’s eye throughout the frame, and creating an illusion that your image is moving. Examples of good use of movement are blurred water, diagonal lines, and stopping motion when appropriate.
The image below uses both of these ideas. The texture gives somewhat of a “vibrating” look, like the forest is moving. The combination of dark and light vertical lines helps to move the viewer’s eye from one side to the other.
This photograph from Fires Creek in North Carolina uses blurred motion of the water to emphasize the constant flow of the water. This is achieved by the use of a long exposure and a tripod.
Lines create movement of the viewer’s eye all around this piece. The spiral naturally draws you back into the frame, where you land on the last circle.
Read about the other Principles of Design.