King David appears half a dozen times in the Koran; his son Solomon is also part of the Torah / Old Testament story that makes up the Muslim Holy Book.
David was not so revered in some schools of thought in Islam because of his entanglement with Bathsheba - murder, adultery were not considered compatible with Islam; in the Koran they do nothing wrong, but some Muslim scholars noted differences in the Christian and Jewish sources, and even went as far as questioning whether he was in fact a Prophet.
On the Night Journey Mohammed met seven Prophets who preceded him in Islamic tradition. Here Mohammed on Buraq is led by an angel towards David and Solomon, which suggests that in the region where this miniature was produced David was venerated.
The page comes from the Mi'râdj nâmeh (The Ascension of the Prophet) by Mir Haydar.
This copy was created in 1436 at Herat in Afghanistan.