Introduced in the mid-19th Century, the pith helmet became Army standard issue to British troops serving in India to protect against the sun. Indeed, the pith helmet became so closely associated with the image of the British in India that it became affectionately known as the "Bombay Bowler".
The pith helmet is a wide-brimmed, domed hat made of cork or pith (dried spongy tissue from certain local flora, such as the sola plant and the paper bark tree), and covered with a light, khaki-coloured fabric. In fact, cork supplanted pith as the construction material of the helmet as it is a more robust, lightweight material which affords a reasonable amount of protection. In addition to head protection and the obvious shade a hat gives, another benefit of the pith helmet is that its cork material retains moisture when immersed in water, thereby keeping the wearer's head cool through evaporation. In addition to a leather chin-strap, a "pugaree" (a small bandana made of cotton) would often be wrapped around the hat's base to add decoration.
The pith helmet entered into more general use when they became the headwear of choice for intrepid explorers such as Stanley and Dr. Livingstone. Several variants are available; French (original), British and American.
I am informed by avalyn that US Mail carriers still wear pith helmets during the summer months.