Supposing you were living in a dream, or a nightmare, or you were a character in the plot of a book or film, or were in some kind of role-playing game or virtual reality system. How would you know? Would you assume it was REALITY, or would you start to suss out there was something a bit unreal about it?
Looking at the perceived reality of the normal world, it's obvious to me there are things about it that are a bit iffy, like it's all some kind of paranoic put-up job. (more about this at the page of Direct Drive)
So, the next question is, what is REAL REALITY like? With a bit of thinking about it it's possible to figure out things about what reality would actually be like if it was the Real version of reality.
The term "Real Reality" used by Zyra has the connotation of this idea which springs from the fakeness of the normality of the perceived world, but also there is the connotation of things to do with things seen in future prediction visions by Zyra, in which "Real Reality" refers to an effectively ideal world, a utopian enlightened futuristic vision.
As Zyra is a paranoid schizophrenic, it is to be expected that Zyra's visions are spectacular and vivid, in glorious schizophrenivision. However, the question of the truth of these visions as actual representations of The Future, etc, is questionable. Being scientific about it, a person isn't automatically right on account of it being a "vision", and they are not automatically wrong on account of being MAD. However, there are things about Zyra's notions of Real Reality which mysteriously seem to fit with things that have since happened. Most notably The Internet.