I'm not a meteorologist, but as I understand it, "wind" is just air moving from a high pressure area into a low pressure area in an attempt to equalize the two. The greater the difference in pressure and the closer the two areas are to each other the faster the air moves. It's not so much that the air moving in different directions cancel each other, rather, when the moving air reaches the center of the low pressure area it loses the pressure differential to push it. The dark blue areas on Windy can be either low pressure centers with wind moving towards it, or high pressure centers with wind moving away from it. The drastic form of this is when a low pressure forms within a high pressure, completely surrounded. This is when the air begins to rotate in towards the center. As the air picks up speed, fueled by heat which thins the air causing it to rise and lower the pressure even more, the low pressure center becomes even lower. Depending on the amount of heat put into this "engine" it can develop into a cyclone or hurricane. Never-the-less, the center of a cyclone is usually a dead calm.
