Reality is variously defined as the totality of everything that exists, or as an aspect of a thing which exists independent of anyone's awareness or perception of that aspect. Reality is independent of the human mind, i.e. reality would continue to be the case whether or not anyone believed it, or indeed whether or not there were any human minds to believe it in the first place.
- "That which, when you stop believing in it, doesn't go away." -- Philip K. Dick
Something that is said to be a "fact" is a concept, statement, thing, scientific law, or event that has been unequivocally (indisputably) proven to be reality, i.e. truth. Facts are always based on concrete, verified evidence which substantiates their reality. However, on the other hand, a too strict application of this procedure might result in a closed-minded materialist worldview. Few would argue that some aspects of reality, namely the divine, should be subjected to a strict materialist critique, because these methods still rely on imperfect human understanding of the world. Combining a reality-based outlook on life in everyday matters while still maintaining a strong reliance on the - no less real - truth derived from higher sources is a reasonable way to realize the potential as well as the limitations of human understanding of reality.
M. Scott Peck described sanity as "dedication to reality at all costs".
Ontology is the branch of philosophy that deals with the study of reality.
An entry in a physics glossary:
- We say that science studies the "real" world of perception and measurement. If we can apprehend something with our senses, or measure it, we treat it as "real". We have learned not to completely trust our unaided senses, for we know that we can be fooled by illusions, so we rely more on specially designed measuring instruments. Yet much of the language of science has entities that are not directly observable by our senses, such as "energy", and "momentum". These are, however, directly related to observables and defined through exact equations. Philosophers may argue whether the "real" world exists, but so long as our sense impressions and measurements of this real world are shared by independent observers and are precisely repeatable, we can do physics without philosophical concerns. 
Monorealism, a term coined by the Church of Reality is a world view that there is only one true reality that includes all other realities, parallel dimensions, universes, next worlds, deities, that are actually real. Everything that exists, that which is real, that which is true, is all part of reality. That which is not real, fiction, imaginary beings, stories, and things that do not exist are not part of reality. In this world view there are two and only two mutually exclusive classes, real and unreal, and everything is in one of these classes and not the other.