ANSWER: What you are referring to only appears once in the Bible, "To the angel of the church in Philadelphia write . . . who holds the KEY OF DAVID." (Revelation 3:7). The speaker is the resurrected Jesus, whom John sees in a vision, and the message is to the church at Philadelphia. Unfortunately, Scripture is silent regard a a direct answer to your question. There is a lot of conjecture and supposition on this subject but one should understand that the Bible does not specifically identify this object.
The one thing that made David unique was the promise God made to him. God, speaking through the prophet Jeremiah, prophesied of the descendent who would bring salvation and confirm His covenant with all.
14 The Lord said, “The time is coming when I will fulfill the promise that I made to the people of Israel and Judah. 15 At that time I will choose as king a righteous descendant of David. That king will do what is right and just throughout the land . . . I will choose one of David’s descendants to rule over the descendants of Abraham, Isaac, and Jacob. I will be merciful to my people and make them prosperous again. (Jeremiah 33:14 - 15, 26)
Some have speculated that the covenant would require a physical descendent to be ruling over at least some portion of Israel down to our present time. One explanation of this can be found in Judah's Sceptre and Joseph's Birthright, written by J. H. Allen. He makes a powerful case for the lineage of rulers existing today.
The problem with considering this to be a physical, ruling king of the present time is that the covenant also covered the Levites (Jeremiah 33:18). We know that since the time Jesus became our High Priest, the Levitical priesthood has had no function (see Hebrews 7 - 10). Some have explained this problem by saying that Jesus, a descendant of King David through Mary, now rules over "spiritual Israel," the church, and will in the future once again physically rule over Israel on this earth. That still does not explain the question of the promise of the Levitical priesthood remaining functioning and offering burnt offerings and sacrifices.
A key was often worn on the shoulder of those who possessed official authority and power (see Isaiah 22). In the New Testament they were also symbolic of these traits. In Revelation, Jesus is said to have several of them which unlock death and hades (or the grave, see Revelation 1:18). An angel, also in Revelation, is given one to lock the spiritual cell or 'bottomless pit' where a bound Satan will be constrained for one thousand years (Revelation 20:1). This evidence points to this object representing, at least figuratively, the possession of power and has nothing WHATSOEVER to do with Biblical prophecy.
Thankfully, Jesus and His apostles have given us the plan for our salvation and that salvation DOES NOT depend on the "key of David" and our interpretation of what it is. It is, indeed, one of the most fascinating areas of study in the Bible but we should not claim to know for certain what this means. Each of us will have to decide for himself the spiritual meaning of this object.