I've discussed this one before, but my thoughts have evolved to the point of needing a new post. What is existence? What does it mean to exist? The study of this nonsense is known as Ontology and it's officially a branch of metaphysics. It's not a question many people ask, because, why bother? I do ask the question because it bears on many other areas of inquiry, including very important areas such as epistemology.
I would recommend reading the Wikipedia entry on Ontology, as it will help explain the various areas of study and thus provide you with the foundation to criticize my ideas.
Basically, in discussing being, we have three aspects of existence that play different roles: intuition, sensory experience, and language. They are of equal importance.
First and foremost, existence is linguistic. "To exist," are simply words and the meaning of those words is how they are used.
I think that language is fundamentally representative. It always represents something to the user of those words. Even words such as "oh shit," represent internal states. The word itself evolved from external usage between people, but it is used to represent something internal. For example, "I am scared" represents to the user an internal state that is inaccessible to those hearing the word. From the listener's perspective, the phrase "I am scared" represents a series of behaviors: hiding, cowering, sweating, etc.
As would be expected based on this model, I think that most words are a mixture of internal and external representations. I also think that this very mixture is the reason why the term existence is so contentious and hard to nail down. In conversation, our intended use frequently vacillates between an internal sense of what the word means and the external reality to which it must be tied when being spoken.
I think that existence has two types, real existence and metaphysical existence. I use the term metaphysical when referring to a concept that seems true yet is outside our ability to know.
For example, I climb a ladder, place a ball on top of a book shelf, and then get down. I can no longer see the ball, detect any shadows, or in any way know that the ball is there. For the sake of this argument, you shall be an omniscient third person, and the ball is actually on the book shelf. From my perspective on the ground, does the ball still exist?
Yes and no, and this is the root of our problems with the word. In reality, it does not exist. It only exists when I sense it, and even then, it only exists insofar as I am sensing it.
Continuing the example, let's say that I see the ball. Does the ball have texture? Metaphysically yes, but realistically, no. Let's say that I am touching the ball (*giggle*) with my eyes closed. Does the ball have color? Metaphysically yes, realistically, no.
This segues into the final element of the gestalt of our conception of existence: intuition. Intuitively, the ball is still on the book shelf. This intuition is called object permanence and it is something that we learn at a very young age. This intuition becomes one of the underlying principles upon which the framework of a human perspective on the world is built. Basically, the rule states that "there are things that exist that I do not currently sense."
For example, "there exists a planet that is covered entirely with frozen methane, under which is a liquid sea of methane where bizarre life forms swim about". This statement is either true or false. We can never know if it is false, and we only know if it is true if we find the planet. We then use intuition to say that the statement was always true. It was metaphysically true, which is completely useless. The complete intuitive concept is that "there are things that do and do not exist which I do not currently sense."
This sense is entirely internal. It is ineffable. I cannot explain the intuitive sensation about the existence of things outside of sensation, but this is identical to being unable to explain the sensation of hunger or the color red. But like we want to use red as though we are communicating our internal state, we are driven to use the term "exist" in the intuitive metaphysical sense. Other people accept this nebulous usage because (assuming the existence of other minds and their similarity to my own) we all have the same intuitive sense of things existing outside our sensory sphere.
These things do not exist! There is no way that they exist. They might eventually exist once we sense them, but they do not when in a Schrödinger's cat state of indeterminate existence. Truly, the famous cat thought experiment was created specifically as physicists dealt with the ramifications of understanding that things do not exist until we sense them.
Thus, the intuitive sense of things existing separate from sense or language is explained as a wavefunction of probability in modern physics. The wave collapses into a determined state (exist/not exist) only upon an observation. This is the nature of reality. Nothing exists unless I am sensing it, and even then it only exists insofar as I am sensing it, be it with sight, hearing, smell, or touch. Beyond that is intuition about the nature of reality that we learn as a child. Beyond that intuition is a word that means only how we use it, and we can only possibly use it to describe things to which all users of the word have access, namely, empirical reality.