From the earliest of times in Eastern cultures it has been a sign of respect to cover the head. Ancient head coverings for men came in various sizes and shapes. Ancient Syrians are depicted on Egyptian monuments wearing a cloth with a fillet of rope. Certain sculptures show the Assyrians wearing a cloth around the head, like a turban. Daniel mentions the Babylonians wearing "hats", which were also like turbans.
The above sketch is a modern Arab Bedouin wearing a large cloth on his head, it is square and folded into a triangle, this is the "keffiyeh." Notice the rope (fakal) around the top holding the head cloth in place, this was is made of wool or twisted goats hair.
In ancient Israel there seems to have been no covering for the head except on certain occasions. For example, during times of great distress it was customary to wear a head covering. Remember when Haman was found mourning and with his head covered? Also during times of war, the Hebrews wore a helmet made of leather.
During the time of Jesus, Jewish teachers would always have their heads covered in public, as a sign of righteous reverence. They apparently wore the "sudarium" (white linen cloth), wound round the head as a turban, with the ends of it falling down over the neck. Common people sometimes wore a cloth with a band, or just a band in warm months.
Today religious Jews wear the Yarmulke ("kippa" in Hebrew), because it is believed that by covering the head during prayer, one showed respect for God.
"And their nobles have sent their little ones to the waters: they came to the pits, and found no water; they returned with their vessels empty; they were ashamed and confounded, and covered their heads. Because the ground is chapt, for there was no rain in the earth, the plowmen were ashamed, they covered their heads."