A hurricane's eye is calm because this quiet center is the hub around which the section of strongest winds forms. Without this hub, the storm would not develop the necessary power. The rotating winds cause the updrafts of air that give a storm hurricane strength.
Within tropical storms, the forces of convection send bands of air, heavy with vapor, spinning around a shared central area. As the speed of the rotation grows, the band begins rotating even more strongly at a certain distance from the center of the storm. This band is what forms the eyewall, or the protective barrier around the hurricane's eye, which becomes an area of calm.
As the winds rotate around the eye, they send air moving up from the surface of the water to the very top of the storm. The air moves outward to the edges of the storm before moving down. This becomes a cycle that makes the storm develop further. However, some of this air returns back down through the center of the storm, keeping the eye free of rain. The combination of dry weather and protection from winds causes a calmness in the eye. For those experiencing the storm on the sea, though, the eye is a place where waves collide from all sides, building waves that grow as high as 130 feet.