The single most important aspect of our forward stroke is torso rotation. When we rotate our body it is engaging core muscles which are much larger and stronger than our arm muscles. This rotation also allows us to incorporate our legs which are braced in the kayak attaining even more power. If we fail to rotate our torso we instinctively engage our arms, pulling the paddle through the water. I have often thought about ways to illustrate this, and make it easier for new paddlers to understand what I am trying to explain. Here are some visuals to help you understand.
First, imagine sitting in your cockpit, with the face of a clock around your waist. Your spine is the center of the face where the hands of the clock are joined. 12 o'clock is the very center of the front of your cockpit. Now imagine a pencil stuck in your belly button. With each paddle stroke the point of that pencil should move from 10 o'clock on the left, through midnight to 2 o'clock on the right, and then back again to 10 o'clock.
10 to 2 and back to 10 on each pair of strokes.
Another useful visual is your hands. With the top hand, the one pushing on each stroke, try reaching to 10 and two on each stroke. If you keep your hands closed around the paddle, imagine punching to your left and right. I try and keep my hands open - thus relaxed - and so I think about reaching for 10 and 2 on each stroke.
Another visual cue is this. Your top hand should move across your face - I like chin height - this will emphasize the rotation and help you have good posture. With your hands low we will tend to slouch, and this will decrease the amount of power we transfer from our core to the water.
When I get tired, my hands tend to drop, which in turn lowers the amount of power coming from my core and legs. Which in turn increases the amount of work I am doing with my arms, which will then make me more tired.
On my first trip to Alaska as a student, We had a particularly long day, that involved paddling to a massive waterfall. We had trouble finding a campsite that was big enough for the size of our group without having a negative impact on the surroundings. We searched many potential locations and many hours later (14 I think) We finally found a site, and as everyone was setting up camp my Sifu came around and said to each of us 'if your arms are tired, your paddling wrong'. This stuck with me, and whenever I feel tired, I analyze what I am doing. Is my posture correct? Am I rotating? Are my hands relaxed?
There is another check I still use on occasion that I call the Frankenstein. The next time you are paddling, lock your arms straight. And then paddle. With your elbows locked straight the only way to propel a kayak forward is by rotating your body. While this may look silly, it emphasizes what the body rotation feels like. When you can feel your body rotating, go back to your normal stroke, are you still rotating? On long days I will throw in a couple of 'Frankenstein' strokes just to check.
Speed doesn't come from big powerful arms, it comes from good rotation and using your legs. Watch the video linked to below, and you will see these Olympic paddlers rotating furiously, and in some of the shots you can even see their legs pushing up onto the skirt attached to their very narrow boats. Around the 40 second mark is a great example of rotation in slow motion.