Located just outside of the eye is the eye wall. This is the location within a hurricane where the most damaging winds and intense rainfall is found. The image below is of a hurricane (called cyclone in the Southern Hemisphere).
Image by: OSEI
Eye walls are called as such because oftentimes the eye is surrounded by a vertical wall of clouds. The eye wall can be seen in the picture above as the thick ring surrounding the eye.
At the surface, the winds are rushing towards the center of a hurricane -- forcing air upwards at the center. The coriolis force acts on these surface winds, and in the Northern Hemisphere, the deflection is to the right. The convergence at the eye wall is so strong here that the air is being lifted faster and with more force here than any other location of the hurricane. Thus, the moisture transport from the ocean and subsequent latent heat production is maximized.