Sine wave motion in Taekwon-Do is characterized by an up and down motion of the body. The force delivered through blocks and strikes is increased by dropping the body into the block or strike immediately prior to and at the moment of impact.
This effective use of body weight provides an increase in velocity resulting in increased power delivered to the target through the blocking or striking tool.
Sine wave motion also enhances the flow and beauty of movement so characteristic of Taekwon-Do.
GM Donato Nardizzi has created an excellent series of videos explaining sine wave motion. I have copied the first one here and have links to the rest, well worth watching if you want to understand sine wave motion and how it forms the backbone for the theory of power.
Taekwon-Do Science: Sine Wave Motion #1
This is the first video of the Taekwon-Do Science series which explains the scientific principles of Taekwon-Do. In this video, GM Nardizzi explains what a sine wave is and how Taekwon-Do sine wave motion is similar to a sine wave.