The Last and Best Theory
Short version: Ash is a conscious program in a VR world; she's just computer code, but she has free will and a soul as much as we do. The game Avalon is designed to find the "best" such AIs and offer them a chance to be promoted into full, embodied reality. That is the journey to Avalon. (And, yeah, it's at the same time a flat-out religious metaphor.)
All of that can be inferred from the movie. From the above, we can infer that the true world of Avalon is far-future, ultimately utopian, but severely depopulated. It may be on a post-apocalyptic Earth, but it may well be a space colony somewhere in the Pleiades, the star cluster named after the Seven Sisters of Greek mythology. Perhaps physical reproduction doesn't work as well as it ought to. Our descendents have built Ash's reality in order to add worthy souls to theirs.
Ash's reality is based upon an actual dystopian near-future that humanity passed through on the way to this utopian future. The Avalon war game is in most ways a copy of the actual war game that people played to escape this dismal reality. IOW, the opening text exposition is true. The (amazingly smart) catch is that we are not watching that reality, but a simulation of it created much later.
Note that the AIs that populate Ash's reality are being given an opportunity to do just what the actual humans of that time did: escape the reality to find something better.
The "Special Class A" level (known as "Class Real" only to embodied humans) is a VR based on ancient records of turn-of-the-21st-century Warsaw. Why? Why not? Perhaps one of the chief designers of this multi-level VR is of Polish ancestry and possesses and cherishes filmed records of the city. It is, of course, the final testing ground for AIs, to see if they are worthy of promotion to embodied reality.
I'll lay out the evidence and flesh out the created world in the reply.
Prepare your minds for a new scale of physical, scientific values, gentlemen.share