Not everyone knows just what a "Goth" is. I have a slight speech impediment and sometimes when I tell folks that I've been to a "Goth club" they think I've been somewhere swinging a club at a ball!
Ask an academic and they might tell you that the Goths were a group of nomadic peoples who (among others) are credited with the overrunning of the Roman Empire in the 4th and 5th centuries. This is true, they did, and for a a while there were Visigoth and Ostrogothic Kingdoms in Europe (until either re-conquered by the Byzantine Empire or succeeded by other dynasties).
Gothic Architecture is mostly know for a church building style -- we tend to think of vast cathedrals with huge vaulted ceilings, and stained glass windows. It's more likely though, that at this website, I mean something more like the definition given by Tony Thorne in Fads, Fashions & Cults(1) (which focuses mostly with American and English culture):
One strand of punk imagery -- exemplified by the groups Sioxsie and the Banshees and the Damned -- consisted of doom-laden or anthemic guitar-based rock music accompanied by black clothing, bleached hair, powdered faces and the wearing of occult or mock-medieval paraphernalia. This horror-film iconography preceded Punk; it had been used by a variety of performers(2) since the 1950s as well as comic books and the camp Sixties The Addams Family and The Munsters. In the post-punk era the humorous aspects of the style were picked up by such neo-psychedelic bands as Gaye Bikers on Acid and Zodiac Mindwarp, as well as the enduring Damned. The introverted and serious vein evolved via groups such as Bauhaus, the Cure, Southern Death Cult, Nick Cave and the Bad Seeds and the Sisters of Mercy to become Goth.
The term itself (based on 'Gothic Rock', a music journalist categorisation) began to be used in 1984 of a youth cult that had during the previous year been focused on the Batcave, a Soho music club. This had been touted as a revival of Punk values but although its label 'Positive Punk', and its leading exponents, Brigandage, did not last long, the Goth pose of pallor, black leather, crucifixes and a sort of morbid passivity caught on among adolescents. Goth proved to be the most enduring direct legacy of Punk, but without Punk's energy, anger or subversion. At its edges it blurred with grebo or crusty culture, but its mainstream presented a remarkably unified appearance and attitude; an impressively forbidding fantasy mask for youth angst and sensitivity. (p98)
Now I bet there's some out there that'll disagree with this definition -- fair enough -- it isn't mine, but is one that can be useful for some purposes. Personally I think that the Goth sub-culture is just another example of Gothic Revival, something that's been going on for the last 300 years. This is just the current wave, reflecting modern mass culture.
This wave merely gained momentum in the late Seventies and early Eighties, when people realised that you could whoever you want, and still belong; that you could dress up without being "glam" and express sensitivity and sexuality in ways other that mainstream. For Goth is certainly not mainstream, merely easily identified from outside.
So a Goth is (more or less), someone who follows the Goth scene, or Goth sub-culture. Clear (as mud)? Good. Don't lose any sleep over it.
Thorne, Tony; FADS, FASHIONS & CULTS: From Acid House to Zoot suit -- via Existentialism and Political Correctness -- the definitive guide to (post-) modern culture
; London, Bloomsbury Publishing, 1993; ISBN 0-7475-1384-8.
(2) Such as: Bobby 'Boris' Pickett and the Crypt-kickers; Screaming Lord Sutch; the Undertakers; Hawkwind; Black Sabbath; Alice Cooper; and The Rocky Horror Show.