For a useful working concept, we can define reality as that which is qualitatively experienced by an aware mind and quantitatively modeled by science. Accordingly, we can describe reality as a spectrum that spans in two directions: one way into the more abstract, quantitative, and objective; the other way into the more concrete, qualitative, and subjective.
At the one extreme, we have pure mathematics and a conceptualization of the world as a mathematical object—perhaps an intricate quantum graph or some other structure that I really have no business talking about, given my limited knowledge in this area. At the other extreme, we have pure awareness and the world as a manifestation of consciousness; there we are in the realm of spirituality.
In between, we have all the different sciences with varying degrees of hardness. For example, as the principal “hard” science, we have physics—very close to mathematics—and something like neuroscience a bit more to the right. On the other side of the spectrum, we have, among many others, psychology, followed by phenomenology and suchlike, which are increasingly focused on subjectivity and qualitativeness. Somewhere in the middle and leaning partly to the left, partly to the right, I would locate my own academic background: the field of cognitive science.
For practical purposes, the left side is more useful for outer engineering (building things), while the right side is more useful for inner engineering (developing oneself).
But remember that all these fields and sciences are just language games we humans like to play, even if accompanied by highly technical methods. Towards the left, we play these games at lower levels of descriptions of “the Universe” or even “the mathematical universe,” according to a hypothesis of the same name proposed by Max Tegmark. Towards the right, we move to higher and higher levels until we climax conceptually, mystically with the word “God.” Actually, though, our natural languages collapse at the endpoints: either into pure formalisms or into a Zen-like rejection of words and concepts altogether.
Now, when we look past the differences, we see that all these language games are ultimately describing one and the same thing. “God,” “the Universe,”… these are different words for different perspectives, yet unanimously pointing at that which we could just as well call “nature,” “existence,” “the world,” or—to come full circle1—”reality.” In the end, the words don’t matter; what matters is what we do with them.