He placed His right hand on me, saying, “Do not be afraid; I am the first and the last, and the living One; and I was dead, and behold, I am alive forevermore, and I have the keys of death and of Hades." Revelation 1:17b-18
When it is said that a person holds the key to something the meaning is relatively straight forward. They have the means and therefore the power to unlock what is locked, they have authority over it. To say that Jesus has the keys to death and Hades is to say that he has the ability to open the door to death and Hades and the power to release those who were locked in behind it. Jesus has authority to release people from death and Hades.
Death is the common fate of all the living. When anything living crosses that threshold, whatever animated its life is lost to its physicality. If that life isn't reinstated quickly it never can be, it's locked up behind death's door. For humans, that impelling, animating something is called a soul, an incorporeal, spiritual essence which carries not only the life force, but the personhood of the human.
Before Christ's ascension, humans souls were locked in Hades (Sheol in Hebrew) upon death. The body turned to dust and the soul was locked in Sheol. There is some thought that Sheol really just meant the grave, but I think Jesus' teaching concerning the rich man and Lazarus completely undermines such thoughts. Jesus envisioned Sheol as a place where dead people were kept self-aware, conscious. Whereas it may have been "restful" for the faithful, Jesus revealed that it was anything but for the unfaithful.
Once in either condition, there was no way out. Death and confinement thereafter in Hades was a one way trip. Jesus, however, overturned the order of all that had gone before and did what no one had done before or since. He entered into death and Hades, and then, of his own accord, he came back. His authority and power over death and Hades was thus neither theoretical nor derivative--it was demonstrative. He went there and came back with captives in tow, that is why he is said to have the keys of death and Hades.
There are not literal keys in Jesus hand, of course, as if he required a tool to open that figurative door. His power is intrinsic to who he is. The keys are merely a figurative way to put the concept into graphical terms. Jesus, the Son of God, has power over life and death, what was irreversible to everyone else is reversible to him. The most impenetrable, intractable wall humanity faces, death and Hades, Jesus had the power to walk right through, and most importantly for us, he has the power to bring others with him.
The phrase, "the key of David," elicits similar thoughts as did the phrase, "the keys of death and Hades." In both phrases, the word key relies upon the same basic symbolism which refers to the possession of authority. Whereas the first expression has an inherent Jewishness to it, the second is markedly Greek (Gentile). Regardless, what is in focus is an eschatological, teleological authority--the possessor of the keys has authority to affect and effect the end of things.
The symbolic connection to the New Jerusalem is obvious. The Messianic heir to David (Jesus) is the one in authority over the New Jerusalem. He has the power to let folk in or to keep them out (see Matthew 16:18-19 for an interesting connection and extension). If entry into eternity with God is something one desires, one will have to come to Jesus and get his approval in order to enter. Thankfully, to be coming to him is all that it takes to get it!
Though there is nothing particularly Jewish about Philadelphia, it was in the message to that church that this Jewish nomenclature was used. In the Kingdom of God, neither Jewishness nor Gentileness matter a whit, despite the fact that there is distinctive historical tracks for Israel's redemption and for that of the Gentiles. I don't think much can be read into that, for the new Jerusalem is of infinitely greater import than the original, and it is to that the symbol actually points.