Torso rotation
From KayakWiki
Torso rotation means basically that you rotate your body from the waist. However, sprint and marathon paddlers rotate below the waist. They rotate on the seat using leg push on the active paddle side and often sit on a rotating seat. You can see that a paddler is rotating the torso by observing the zipper, say, on the PFD - it should move side-to-side quite a bit. But more telling is to watch the side of their hip in an ICF K-1 to see the hip moving fore and aft as the legs extend.
Almost all but the well-trained sprint and marathon k-1 paddlers DO NOT rotate no matter how much they think they do. It's easy to fool yourself, but if you are not spinning back and forth on the seat you are not rotating in the method that delivers a real power to the stroke that comes from the legs. Push the boat forward via the bottoms of one foot at a time and not from the seat of your butt. Rotation in the stroke is brought to the rec sea kayaker via the race world but in almost all cases is taught by instructors with no real knowledge of proper racing stroke and gets dumbed down in the process. This is a real shame because instead of providing good instruction it just spreads this misrepresentation. It's almost better if they did not try to teach the forward stroke.
The reason for using torso rotation is that the torso muscles are large. These are capable of working for long periods of time generating large amounts of work. Arm muscles, on the other hand, are smaller and are better suited to lower levels of output for shorter periods of time. However, arms can be moved faster and at very high stroke rates. If you watch a top sprinter at a race start, you will see that they are all arms for the first few strokes till they get their boat up and out of the hole, and moving at higher speed where they transition into full rotation using the legs and back and abs via rotation. If you try to paddle using only your arms, you will limit your speed and endurance.
One problem that some paddlers have is that they strive for torso rotation but actually perform only shoulder rotation. That is, they are rotating their torso somewhat but the major portion of the motion and work is coming from the arms rotating at the shoulders. While stronger and having more endurance than just the arm muscles, shoulders do not have the power that the torso has. This is the mistake of watching the zipper on a pfd, its being moved mostly by the shoulders, and not true rotation from below the waist. In the end, shoulder rotation can create the illuusion for the paddler that they are getting some rotation, but only the full seat top rotation, even if only slight, will employ the full power of the legs.

