The eyewall is generally the part of the hurricane that has the strongest winds. By contrast, the center of the hurricane, also known as the eye, has relatively light winds.
In a mature hurricane, the stronger surface winds tend to move inside the center of the storm, forming a circular column around the storm's eye that is known as the eyewall. It is typical for the heaviest rain or other precipitation and the most violent winds to be found in the eyewall. The most destructive part of the storm in the Northern Hemisphere is generally the eyewall section to the right of the storm's eye, which is generally where storm surge comes from.