Generally what we understand by 'reality' is the world of 'physical' objects, but also abstract-seeming notions such as space and time. Mind is not 'real' in the same sense. It is considered by many to be a secondary kind of reality, probably an emergent property of matter, similar to information. Consciousness may be epiphenomenal, that is, having no influence on the way that our bodies behave beyond what physical laws demand, having no additional 'reality' to the matter generating it. Some philosophers, argue to the contrary, that the mental world is primary, and the material world secondary and emergent. They claim primacy for the mental by virtue of the fact that we primarily inhabit the mental. To avoid an unpleasant solipsism they do not usually deny the reality of other selves. Roger Penrose (Prof of Maths at Oxford Uni) sees the notion of the primacy of mental reality, and the emergence of the physical from consciousness, as lopsided.
"Even if such a solipsistic basis is not adopted, so that the totality of all conscious experience is taken as the primary reality, I still have great difficulty. This would seem to demand that 'external reality' is merely something that emerges from some kind of majority-wins voting amongst all of us taken together. I cannot see that such an emergent picture could have anything like the robustness and precision that we seem to see outside ourselves, stretching away seemingly endlessly in all directions in space and time, and inwards to minutest levels that we do not directly perceive with our senses."
Penrose recognises that the emergence of consiousness (by which I guess he is talking about subjective, personal experience) from the "seemingly purely calculational, unfeeling and utterly impersonal laws of physics that appear to govern the behaviour of all material things" is problematic and mysterious. But he also points out that these laws are incredibly precise and intricate.
The 'physical' objects that we think of as most real (say a table) are composed of atoms, which are composed of more elementary particles which have an indeterminate reality. They seem to exist only as solutions to mathematical equations. One of the things that makes quantum mechanics really strange is the notion that all electrons, for example, are indistinguishable from one another: we cannot talk of 'this electron' and 'that electron', but only of the system they inhabit. At its most elemental level, perhaps, the physical may be mathematical information - similar in its reality to consciousness. Of course, it may turn out that there is something not quite right with present-day quantum theory, and a notion that is more in accordance with our experiences may emerge. There is no sign of this yet however.
Penrose writes that "many philosophers would argue that mathematics consists merely of idealised mental concepts, and if the world of mathematics is to be regarded as arising ultimately from our minds, then we have reached a circularity: our minds arise from the functioning of our physical brains, and the very precise physical laws that underlie that functioning are grounded in the mathematics that requires our brains for its existence." Penrose seeks to avoid this immediate paradox by allowing the Platonic mathematical world its own timeless and locationless existence. while allowing it to be accessible to us through mental activity.
Penrose allows for three different kinds of reality: the physical, the mental and the Platonic mathematical, with something, (as yet) profoundly mysterious in the relations between the three. Penrose concludes that we cannot properly address the question of the reality of the physical until we understand its connection with the other two realities.