Gaiters have nothing to do with alligators.  However, technically they can be worn over your shoes & lower section of your pant let as you walk thru a swamp looking for gators.  They will NOT protect your foot or leg from alligator bites.

Gaiters are a type of clothing worn over the shoe and lower pants leg.  This type of garment is worn primarily as personal protective equipment for the lower part of the wearers leg.  Similar garments used primarily for display are spats. Originally, gaiters were made of leather. Today, gaiters for walking are commonly made of plasticized synthetic cloth such as polyester. Gaiters for use on horseback continue to be made of leather.

Gaiters fill the same function as puttees, a part of numerous military uniforms. Gaiters known as jambieres (derived from the French word jambe for legs, hence leggings) were part of the uniform of Zouave infantry regiments.

Gaiters are a type of protective clothing for a person's ankles and legs below the knee. Gaiters are worn when walking, hiking or running outdoors amongst dense underbrush or in snow.  In snow conditions they can be worn with or without snowshoes.

Gaiters strap over the hiking boot and around the person's leg to provide protection from branches and thorns and to prevent mud, snow, etc. from entering the top of the boot.

Gaiters may also be worn as protection against snake bites.

During the 19th century gaiters for riding horses typically were known as riding gaiters.