A shemagh (also spelled shumagh) is a red-and-white checkered version of the keffiyeh, the traditional square headscarf worn mainly by men in parts of the Middle East. Encyclopaedia Britannica describes the keffiyeh as a headdress typically made of cotton, historically worn by rural farmers to shield themselves from the sun, dust, and sand.
Britannica notes that the red-and-white shumagh is most commonly worn by members of the Bedouin community, and that in the 1930s British officer John Bagot Glubb made it part of the uniform of the Desert Patrol of the Arab Legion in Transjordan. It is distinct from the black-and-white keffiyeh associated with Palestine and from the plain white ghutrah worn in Gulf states, which is held in place with a black cord called an iqal.
Source: Britannica, Keffiyeh
Image: Keffiyeh (red-and-white shemagh), Florian Prischl, CC BY-SA 3.0, via Wikimedia Commons.