What is real?
Well that, to quote our ex-president, depends on what your definition of "is" is.
Let us take one mundane definition of existence to start with: Something exists if it is real. If that thing finds form or causality in the Universe, than it is said to exist.
This is quite a good definition of existence! If you can point to it (an apple) or if you can point to its effects (the wind, electricity) than it definitely is a thing
But at second blush, that really is a pretty poor definition. For starters it says nothing about math, or formal logic. If you ask certain philosophers or mathematicians, they will hold up formal logic as somehow being even _more_ real than apples and electricity, for what universe is even possible without causation, implication and set theory? There's an even more obvious hole in this definition too: the Universe itself cannot be said to exist by that definition, for it certainly doesn't exist "inside" itself!
And so we are forced to ponder a reality greater than our universe. What thing can we say about both matter and energy (as above) that we can also equally say about universes and math?
The statement that leaps to my mind is: these things cannot be created nor destroyed.
You can't make another universe in your kitchen , any more than you can destroy Algebra (much to the consternation of students everywhere).
This actually seems a rather good description, as it allows our Universe and matter inside it and logic outside it, to all happily exist within one definition of existence.
Unhappily, this says that an apple (which certainly is created and destroyed) doesn't _actually_ exist. But this isn't really a problem. It can actually help us illuminate:
The concept of Appleness is a form our mind applies to certain collections of atoms and not others (which are the things that actually exist). This fits our scientific view of things quite nicely! While apples certainly perform a nice function in trees and salads, this purely _biological_ and _sociological_ (economic, etc) existence shouldn't blind us to the fact that an apple actually exists only to the extent that it is composed of atoms (which do). Which _also_ isn't to say that biological, etc function isn't important! Apples are amazing! We just shouldn't blind ourselves to the fact that apples are merely collections of atoms.
There is one further, aesthetic argument against this definition: it's full of negations! It only defines existence in terms of what can't be done, or what isn't. To this I say: yes! That's the point! We set out originally to define what is: if I were to use "is" in my definition, that would be pretty circular wouldn't it?
And so we've actually uncovered an interesting fact about the nature and character of statements about Truth and Existence: you can't make satisfactory positive definitions. I've also demonstrated how satisfying a good negative definition can be.
THIS is my answer to those who charge that Science's (and The Buddha's for that matter!) negative definitions of reality are nihilistic. Negative definitions don't render all things meaningless. They merely put the different layers of Truth in their proper order 
 - Well-read readers are aware of modern cosmology and will note that our Universe _has_ a definite starting point (the Big Bang) and are probably ready to dismiss me. My response is that no matter which modern theory of the creation of the universe you believe in, in _none_ of those theories is it possible for you to make _another_ universe. This is what is meant by "can not be created". If you're curious I've explained this for all three major scientific views below:
1) In a "closed" universe which is its own cause (a cyclical big-cruch / big-bang) the big bang wasn't the time of creation, merely the point of re-birth.
2) An "open" universe which is not subject to destruction (the big crunch) is still cause-less (ie without creditability or the ability to be created) even though it does have a definite starting time (the big bang). In this model, because time is a concept native to our Universe you can't talk about what happened _before_ the Big Bang. And if there was no _before_ the Big Bang, there was nothing able to cause it to come into being. The Universe simply sprang into being, without cause or reason.
3) There is one further concept of the universe, which posits that universes _can indeed_ be created and destroyed within the concept of a further "multiverse" which is truly eternal and contains a kind of "foam" out of which universes bubble up. If this is the truth, then our Universe _isn't_ real (by my definition) but the _Multiverse_ most certainly is. Trivially moving "exists" up one rung doesn't negate the argument.
 - http://xkcd.com/435/