It is believed that this is the tomb of the Prophet Dawud (Peace be upon him), who was the father of the Prophet Sulaiman (Peace be with him). Some historians believe that it is not his grave, but “maqam” to designate the place where he once lived.
Dawud (peace be upon him) is mentioned by name 16 times in the Holy Quran.
Dawud (peace be upon him) ruled the children of Israel [Banu Israil] for forty years, seven years in Hebron (al-Khalil) and thirty-three in Jerusalem, who became known as the city of Dawud.
According to the Jewish and Christian faiths (ref: “II Samuel 12:7 -13; Psalm 51:1-19),
"During the period David ruled Israel, there were wars. He was very brave at war. David was also a popular musician, apart from being a warrior. Sometimes when going to the war front as a king, due to age, his captain Joab stepped into his shoe.
One day, there was a war at Ammon, David sent Joab to that war. At home, David was relaxing within his compound. He saw a beautiful woman named Bathseba. Bathseba was the wife of Uriah, one of the warriors who had gone to the battle field to fight. David was attracted to the woman. As a result he called her and started friendship with her until the woman became pregnant.
As the woman was pregnant, David tried to conceal the secret, so he sent for the husband who was at war front to come back home. David, on the following day, gave Uriah a sealed letter to give to Joab. The content of the letter instructed Joab to put Uriah at the hottest spot at the battle field. On the long run, Uriah was killed. This gave David the opportunity to marry Uriah's wife. The woman delivered a male child. Subsequently God sent Nathan to him. Nathan came with a message from God concerning his sin. The message was presented to David by Nathan in form of parable..."
"In Islam, Dawud (peace be upon him) is considered one of the great prophets to whom Zabur (Psalms) was revealed by Allah. The Islamic tradition includes many elements of David’s Jewish / Christian history, for example, his battle with the giant Goliath, but completely rejects his biblical depiction as an adulterer and a murderer.
Dawud (peace be upon him) was the first to know how to make iron armor. Allah mentions in the Sura Saba in the Holy Quran:
“And, of course, We gave Dawud's generosity from Us (and said):“ O mountains! Repeat our praises with him and the birds that you too. ” And we softened iron for him, (saying): “Make wide coats of mail, and carefully measure links and perform righteous deeds.” Of course, I see what you do. ” [34: 10-11]
The Prophet (peace be upon him) said: “The most beloved Salat (prayer) in the eyes of Allah is the Salat of Dawud, and the most beloved Saum (fasting) in the eyes of Allah is Saum of Dawud. He slept during the first half of the night and offered a prayer for one third and slept (again) in one sixth. And he usually observe fast on different days. And when he met the enemy, he never ran. " [Bukhari]
Allah gave him a very sweet voice, one that no one had heard before. When he recite the Zabur (psalms), people, genies, birds and animals, devotedly listened to him.
Sources: Atlas of the Quran – Dr. Shauqi Abu Khalili, Al-Quds – Mohammed Abdul Hameed Al-Khateeb, Stories of the Prophets – Ibn Kathir