A Tenugui (手拭い) is a thin Japanese hand towel made of cotton. It's usually around 3 feet (90 cm), plain-woven and is sometimes dyed with some pattern. It can be used for virtually anything, as a washcloth, dishcloth, but often as a headband, souvenir, decoration, or for wrapping items such as bottles.
Natori Masatake wrote in the Shoninki shinobi manual, that it could be used as a hachimaki headband, wrapped around the head and face, or as a rope for climbing by tying it together with a sash. In other samurai schools it is kept inside the obi sash. In Natori's school it should be folded up and kept inside a collar even when wearing lightweight summer katabira kimono.
According to the Giyoshu military manual, when infiltrating while wearing armor a shinobi should tie a yonshaku-tenugui (four foot tenugui) around the thighs like an outer sash so the armor won't rattle. The same type of tenugui could be used as a military ration when soaked in rice vinegar.