The indentations came first. The original design had no indentations, but cowboys in the Old West combined the traits of tough and gentlemanly. The Stetson company's initial design had a round top, but good manners require a man to remove his hat upon entering a building or passing a woman on the street.
The appropriately attired cowboy would regularly remove his hat by grasping its round crown to remove it completely or to tip his hat to a lady. The constant use of good manners would wear indentations into both sides of the round crown. Hat designers simply saw the natural morph of the crown and altered their designs to better suit the gentlemen cowboys' needs.