The most recognizable feature found within a hurricane is the eye. They are found at the center and are between 20-50km in diameter. The eye is the focus of the hurricane, the point about which the rest of the storm rotates and where the lowest surface pressures are found in the storm. The image below is of a hurricane (called cyclone in the Southern Hemisphere). Note the eye at the center.
Image by: OSEI
Skies are often clear above the eye and winds are relatively light. It is actually the calmest section of any hurricane.
The eye is so calm because the now strong surface winds that converge towards the center never reach it. The coriolis force deflects the wind slightly away from the center, causing the wind to rotate around the center of the hurricane (the eye wall), leaving the exact center (the eye) calm.
An eye becomes visible when some of the rising air in the eye wall is forced towards the center of the storm instead of outward -- where most of it goes. This air is coming inward towards the center from all directions. This convergence causes the air to actually sink in the eye. This sinking creates a warmer environment and the clouds evaporate leaving a clear area in the center.