The Apostle John looked up after his visionary experience as an amanuensis, saw an opened door in the heavens and heard the now familiar voice of his visions calling to him, presumably, through it. We're not told what caught his attention first: the appearance of the opened door, or the voice beckoning him. It really doesn't matter. A new phase in his visionary experience was beginning, and its significance would soon be apparent.
The opened door in the heavens most readily signifies access to what normally would be inaccessible to mankind. In this particular instance that represents access to two things beyond human purview: 1) the throne room, or very presence, of God; and 2) the future. God has to open the door to the experience of either, or the heavens remain closed. So, even though it is not specifically mentioned in the text, that door had to have been opened by Jesus, a key bearer who opens what no one else can open or close.
Doors, opened or closed, serve a variety of roles in the Apocalypse, but the basic concept is the same regardless--doors represent a barrier only authority or power can open. There are doors only God can open (like the one in question), and there are doors that God does not (cannot?) open. That would seem an odd thing, a door barring God, but the Apocalypse represents such a thing existing. Jesus stands knocking, in that case, waiting for the invitee to open the door. The implication for monergism, perseverance, and the whole of Calvinism is troubling, to say the least.
"Come up here," though in the form of a command, was more along the lines of divine commentary and was specific to John (singular). It cannot be related to the Rapture, nor really, to anyone else's access to God or heaven, whether by prayer or other means. Immediately, John was transported beyond the door into the midst of whatever it was opened to reveal. The surroundings were obviously symbolic because God (the Father and the Spirit) were represented tangibly when they are actually incorporeal, and Jesus was represented as a lamb rather than the corporeal form he has taken.