Modern goth (ignoring where the name itself originally comes from) started in the early 80's as part of the punk subculture (which is itself was a rejection of most societal values, and anything considered part of the 'norm').
The phrase was coined by the band manager of Joy Division, Anthony H. Wilson, who described the band as 'Gothic compared with the pop mainstream'. The term stuck, and as punk eventually died, Goth survived and became its own subculture.
The punk clothing and hairstyles mellowed, and the core 'rejection of society' attitude alone lived on in the gothic subculture. Over time this itself has been modified to be more of a 'no more blind acceptance of society's values' as opposed to rejection because it was there to be rejected (and because you could get away with it!).
Movies such as The Crow, and bands such as the Bauhaus helped establish the gothic image as dark, depressing, and even evil. As more and more 'dark' movies came out, numbers in the gothic subculture expanded, and there is now a gothic community in almost every major city around the world, and quite a number of towns have their own representative contingent. Nowdays there are more goth bands around than ever, and it has turned from an 80's phenomenon into a way of life for many people. Unlike the punk subculture that it spawned from, there even exists a class of mature goths, still following the scene around even past their 20's and into their 30's and beyond.