It is actually a Greek word — Ἀποκάλυψις — which literally means lifting of the veil. A more familiar translation is revelation. This, most probably, brings to mind the book from the Bible of the same name. Indeed, the name of the book in the original Greek is Ἀποκάλυψις. Since it deals with the end times, the modern world has come to associate the word apocalypse with a word-ending disaster.
What gets lost in this understanding is that the Bible doesn't just have one apocalypse. It has a plethora. Here are three:
- the burning bush is an apocalypse of the name of God as I AM
- the Incarnation is an apocalypse of God become man
- the baptism of Christ is an apocalypse of God as Trinity
Thus, the term post-apocalypse has a nuance to it that is lost when it is merely understood to refer to what is left after a world-devastating disaster. A post-apocalyptic world is one where God has revealed Himself. This understanding of the word apocalypse can add another a level of richness of any post-apocalyptic D&D world (or any RPG that uses the same sort of end-of- the-world model).
From a Judeo-Christian world-view, the world-shattering event is the Fall. This is then expressed every time humanity turns its collective back on God. The Tower of Babel and the collapse of both the Northern Kingdom (Israel) and the Southern Kingdom (Judah) are examples of this. The apocalypse always takes the form of God steadfastly waiting with open arms for humanity to realize that it cannot find what it most desires without God. He has shown the depth with which He loves us and wants us to be with Him by His willingness to not only become Incarnate, but to go to the cross and tomb.
Thus, a D&D campaign can not only be about trying to rise up out of the ashes of what came before by recovering the treasures of lost civilizations, but a recovery of the apocalypse itself.