Terry cloth is a great material for sweatbands because it is so absorbent. The absorbent qualities come from the nature of the fabric as a looped pile fabric. Terry cloth is made from cotton, but it may be mixed with other materials to offer other qualities.
Nylon is a very versatile fabric used in many ways. It is often used in sweatbands because it is very strong and quite elastic, which makes it great for stretching around a wrist or forehead. Nylon is not prone to collecting dirt, nor does it weaken by sweat.
Polyester is a commonly used fabric known for its strength and durability. Because polyester doesn't wear or deteriorate easily, it is often used in sweatbands and other workout attire.