Albert Barnes Commentary 2 Samuel 15:30

"And David went up by the ascent of the [mount of] Olives, and wept as he went up; and he had his head covered, and went barefoot: and all the people that were with him covered every man his head, and they went up, weeping as they went up." — 2 Samuel 15:30 (ASV)

His head covered — See the marginal references and Jeremiah 14:3-4; Ezekiel 24:17. This was a sign of deep mourning.