The Du-rag or Do-rag is scarf worn on the head meant to be worn after a hair treatment or to protect other headwear from the hair.
The Du-rag became a symbol of a black power movement in the 1960s and later adopted as an African American fashion accessory to wear on its own.
The Du-rag is also used by motorcyclist under the helmet to protect the helmet liner from sweat and greasy hair.
The name Du-rag I've read is actually short for dew or sweat from the head so could be sweat rag. The name as also been associated with do meaning hairdo, either is possible but neither may be true.
The actual du-rags in these pictures are specially shaped scarves with ties and slightly stretchy fabric making them easy to tie onto your head.