When the atmospheric pressure of an area drops, air rushes in to fill that gap. However, when this happens on a large scale, more air will have to travel from longer distances. Due to the rotation of the Earth, the wind will start to turn and spiral into the center of the storm instead of directly shooting into it. This spiraling wind will travel towards to the storm in the lower level of the atmosphere. However, if the air actually did enter the area of low pressure, it would fill the gap and no storm would have happened.
But why do cyclones occur? As we know, warm air rises and cold air sinks. By the time the air reaches the area of low pressure to fill it, it becomes a little too warm. So instead of entering the area, it rises up, rapidly When the storm is over sea, this air will carry lots of moisture which will power the thunderstorms around it. As this air reaches a significant height, it will again spiral outwards, pushing the thunderstorms away from the center. Within the center of the storm, COLD air rapidly sinks, creating a hole in the cluster of thunderstorms. Since there is no horizontal movement of winds in this area, no damage is done. This area is known as the EYE of the cyclone.