Gothic punk style (also defined as 'deathrock' and part of the 'post-punk' movement) deals with themes of death and mortality, sorrow, despair, surrealism, fantasy, the darker side of the life of society, the supernatural, the occult, romanticism, the effects of psychological terror and trauma - just to name a few of the basics.
Gothic Punk The music of gothic punk, (as opposed to the more traditional extremely fast and anger-based hardcore punk), usually exists within the realm of medium-fast, more danceable rhythms often including tribal tom-based drum sections for the verses.
The music also often includes a synthesizer to accompany the drums, bass, and guitar, which again, is something more traditional hardcore punk usually refrained from including. The result is more of a moody, introspective sound that takes one into the realms of imagination.
Gothic Punk ClothingThe classic, essential deathrock (or goth punk) bands include Christian Death (the original lineup with vocalist Rozz Williams), early TSOL, UK Decay, The Damned, 45 Grave, Alien Sex Fiend, and The Cramps.Keep in mind that there were also several 'dark punk' bands around the same time that, while not maybe being quite as 'gothic' in some regards, still had enough stylistic similarities to be worthy of mention.
They include bands such as The Adicts, The Adverts, The Mob, False Prophets, Wipers, Chrome and can't forget classics that bridged the gap between hardcore and dark punk such as Black Flag, Dead Kennedys, and The Misfits. One should at least check out the classic gothic punk (or, as I prefer to call them, deathrock) bands before making comments on the genre.
Keep in mind that while all these bands have similarities, they also have very distinctive sounds that set them apart from the others, as all good artists should, so don't think that just because you've heard one or two of the bands mentioned that you know what gothic punk sounds like. Modern gothic punk bands worthy of mention are Cinema Strange and Cauda Pavonis.