The Nephandi are dark Mages who seek to destroy reality, rather than merely reshape it.
Most, known as Barrabi, have for whatever reason decided to willingly corrupt their own soul in order to gain the power to destroy the world. Perhaps they have been profoundly unlucky in love, or otherwise grown to hate themselves and everyone around them, but they made the conscious choice to do evil. Rather than seek Ascension, they seek to descend, via a process known as the Caul, involving building a shrine of darkness and blood, generally decorated with the dismembered body parts of multiple innocent victims.
Others, known as Widderslainte, are unfortunately not given the choice to become Nephandi, but rather inherit the reincarnated soul of a former Nephandi, an inverted Avatar that seeks descent rather than ascension. Even before their awakening, they tend to be bullies, torturers of small animals, child molestors, or even serial killers. After their awakening, they become even worse.
Before Gehenna, the Nephandi had an organization of sorts, with links to the Sabbat and the Black Spiral Dancers. However, during the War of Gehenna, this formal organization was crushed by the Technocracy and the Tech Infantry, with some cooperation from the Camarilla. There are still a few Nephandi or would-be Nephandi out there, but they are insane loners rather than an organized conspiracy.