'Head Covered' in the Bible

And David went up the ascent of the Mount of Olives, weeping as he went, with his head covered and walking barefoot [in despair]. And all the people who were with him covered their heads and went up, weeping as they went.

Then Mordecai returned to the king’s gate. But Haman hurried to his [own] house, mourning and with his head covered [in sorrow].