This question seems to be the bane of any Goth's existence. Anyone who regularly dresses in black and has a spooky nature will inevitably be asked this question at least once in their lives, if not several times a day. Though there are many different answers and opinions, I'll try to answer the Big Question as best that I can, and explain what Goth is to me.
Why is this question so difficult to answer, you may ask? Well, picture going up to Stephen Hawking and asking him what Physics is. Unless you have a few hours or days of free time, he won't be able to give you much more than a simplified definition that really doesn't cover everything. The same can be said of The Question when it is asked of a Goth (by someone in line a the grocery store, or some instance like that). People expect a short answer, and there really is none.
I could go into a lengthy explanation of Goth being born from the Punk movement in the UK in the late 70s, early 80s, but in the grand scheme of things this really isn't that important. Suffice it to say that a quick search of Google will yield you an accurate enough technical history.
Goth is like celebrating Halloween every single day of the year. A great majority of us where black a lot, incorporate spooky imagery into our outfits and personal spaces, and generally act a bit dramatic. So, on the surface, Goth is an appreciation of all things dark, spooky, and macabre, which the mainstream only thinks appropriate to enjoy on October 31st of each year.
Getting down deeper into the analogy, Halloween is the time when the veil between the world of the living and the world of the dead is at it's thinnest. There is a sort of magic in the air. Apply this to Goth, and you get the understanding that there is more to this world than what we see. The understanding of the wholeness of human existence, from the good to the bad to the tragic; Goths understand that we are not happy all of the time, and that maybe being sad isn't always a bad thing that needs to be "cured" with a handful of antidepressants. Everything is not well. Everything is not pastel colors and rainbows. And that's ok.
Goth is also a rejection of the norm. A rejection of modernism. This may apply more to the Victorian/Edwardian/Romantic styles of Goth, but to an extent it could be said of most sub-genres of the subculture. We've chosen to be different because we didn't like what was "normal."
Most of all, Goth is about having fun. Yes, fun. Bats all over your clothes? A skeleton holding your toilet paper? Yes please! And of course there is that awkward moment when you can't find your favorite top in the mass of black in your clothes drawer. There is an inherent ridiculousness in being Goth that I think one must accept or you should go turn in your Goth Card right this moment.