The 10-gallon hat is a large broad-brimmed hat, with a high rounded crown, traditionally worn by cowboys. The origin of the name has never been established but there have been many theories suggested.

The most commonly accepted but incorrect explanation is that “10-gallon” refers to how much liquid could be carried inside the hat. The largest "10-gallon hat" could maybe hold a gallon.

Another probably incorrect assumption is that gallon in “ten-gallon hat” came from the Spanish “galón“ meaning “braid“, so a ten-gallon hat is a hat with a braiding around the brim.

The last theory is the idea that a “ten-gallon hat“ is for the upper classes, different from the lowly sombrero, which was for the lower classes. The phrase “tan galan“ in Spanish is expressed as “so gallant“ in English which means that upper-class cowboys were considered to be more gallant than common cowboys.

While the origin of the term cannot be established, the 10-gallon hat wasn’t even the preferred headgear for most people in the Wild West—top hats and bowlers were more common. The nickname didn’t enter the popular lexicon until the 1920s, when silent film stars like Tom Mix and Tim McCoy helped popularize the oversized hat in Hollywood Westerns.

Presidents like Harry Truman and Lyndon B. Johnson would later use them to cultivate a rustic image while serving as President.

More Info: www.history.com