The boonie hat became popular during the Vietnam War for all of you Vietnam War ring customers when US Special Forces operators began to wear it while they were on patrol in the jungle or out in the boonies.
As you can see it is a bucket shaped hat with a brim all of the way around. They would purchase the hats locally and wear them until the Army started to issue them. The one thing that I liked about these caps is that they had a cord which would keep it hanging to your neck in case the wind blew it off of your head.
The only real advantage that I think this hat offered over the patrol cap is that it shields the neck and shoulders from ths sun also. the Army must have recognized the value in having these hats because they began to allow the soldiers to wear them.