the parts of a hat
The crown, the cylindrical section that rises like a column from the center of the hat that rests on the head. On hats with a firm, well-defined crown, there may be a hatband fastened into place with a bow,. Caps generally have soft cloth crowns. The brim is the plate-shaped bottom of the hat which shades the eyes. The binding is the stitching around the brim which seals the brim. Some specialty hats, like the hunting cap, have ear flaps.
information gathered from my favorite of all reference books: The Macmillan Visual Dictionary