What exactly is metaphysics?

True. So why did you answer it yourself?

"Language is a code of visual-auditory symbols that serves the psycho-epistemological function of converting concepts into the mental equivalent of concretes. Language is the exclusive domain and tool of concepts. Every word we use (with the exception of proper names) is a symbol that denotes a concept, i.e., that stands for an unlimited number of concretes of a certain kind." http://aynrandlexicon.com/lexicon/language.html

"Metaphysics is the foundation of philosophy. Without an explanation or an interpretation of the world around us, we would be helpless to deal with reality. We could not feed ourselves, or act to preserve our lives. The degree to which our metaphysical worldview is correct is the degree to which we are able to comprehend the world, and act accordingly. Without this firm foundation, all knowledge becomes suspect. Any flaw in our view of reality will make it more difficult to live." http://www.importanceofphilosophy.com/Metaphysics_...

In philosophy, Metaphysics means "Philosophy of Being." It is sometimes described as a branch of Ontology (or vice-versa.) The other branches would be what are now considered Sciences, so its use in philosophy now is basically synonymous with Ontology.

The word comes from the title of Aristotle's work on "being." In Greek it means "after Physics. "Metaphysics" was the book published after his book "Physics." In his Metaphysics he basically searches for what essential being is.

There is a second use of the word "Metaphysics" which is where you might be getting some confusion. In the context of New Age ideas and Transcendentalism, "Metaphysics" means something like "beyond science" or "unexplainable by science." This definition you included may be from this New Age X-Files stuff, not Philosophy.

No sir, by the very definition of the word "metaphysics" or "beyond physics," it is the study, or the "science" of elements that are beyond physical observation. But be warned that this is very misleading, the metaphysical of today is a scientific accoutrement of tomorrow. No one can tell you what metaphysics is, it is just the nature of the beast; we can't put metaphysics in a physical frame, and we cannot certainly not give it an absolute definition. Anyone asking you to do otherwise does not properly understand the purpose of metaphysics.