What do we actually mean by reality?
A straightforward answer is that it means everything that appears to our five senses - everything that we can see, smell, touch and so forth. Yet this answer ignores such problematic entities as electrons, the recession and the number 5, which we cannot sense but are very real. It also ignores the phantom limbs and illusory smells. Both can appear vividly real, but we would like to say that these are not part of reality.
We could tweak the definition by equating reality with what appears to a sufficiently large group of people, thereby ruling out subjective hallucinations. Unfortunately there are also hallucinations experienced by large groups, such as a mass delusion called koro, mainly observed in South-East Asia, which involves the belief that one's genitals are shrinking back into one's body. Just because sufficiently many people believe in something does not make it real.
Another possible marker of reality we could focus on is the resistance it puts up: as the science fiction writer Philip K. Dick put it, reality is that which, if you stop believing in it, does not go away. Things we just make up yield to our wishes and desires, but reality is stubborn. Just because I believe there is a jam doughnut in front of me, does not mean there really is one. But again, this definition is problematic. Things that we do not want to regard as real can be stubborn too, as anyone who has ever been trapped in a nightmare will know. And some things that are real, such as stock markets, are not covered by this definition because if everyone stopped believing in them, they would cease to exist.
There are two definitions of reality that are much more successful. The first equates reality with a world without us, a world untouched by human desires and intentions. By this definition, a lot of the things we usually regard as real - language, wars, the financial crisis - are nothing of the sort. Still, it is the most solid one so far because it removes human subjectivity from the picture.
The second equates reality with the most fundamental things that everything else depends on. In the material world, molecules depend on their constituent atoms, atoms on electrons and a nucleus, which in turn depends on protons and neutrons, and so on. In this hierarchy, every level depends on the one below it, so we might define reality as made up of whatever entities stand at the bottom of the chain of dependence, and thus depends on nothing else.
This definition is even more restrictive than "the world without us" since things like Mount Everest would not count as part of reality; reality is confined to the unknown foundation on which the entire world depends. Even so, when we investigate whether something is real or not, these final two final definitions are what we should have in mind.