A dark hatband on a straw hat.
hatband definition by Webster's New World
Webster's New World College Dictionary Copyright © 2010 by Wiley Publishing, Inc., Cleveland, Ohio. Used by arrangement with John Wiley & Sons, Inc.
a band of cloth around the crown of a hat, just above the brim
hatband definition by American Heritage Dictionary
A band of ribbon or cloth worn on a hat just above the brim.