I found this article rather confusing and it sent me searching for a more straightforward explanation of how exactly the watch calculates how many calories you’re burning for the move ring in Activity. Here, from Reddit, is an explanation that is so straightforward as to be obvious:
Basically, you enter in your mass. The watch calculates about how active you are based on motion from the accelerometer and the heart rate meter. Then, using statistical models that they have generated from other people, they give you a calorie count.
That last sentence is odd. Where do the statistical models come from? Turns out Apple has a whole lab specifically dedicated to this.