The Black Hand was a shadowy organization of Vampires who formed the shock troops of the Sabbat in their ongoing war of Blood against the Camarilla. They used assassination, kidnapping, terrorism, diablerie, mind control, and magick to fight both the Camarilla and human Vampire-hunting organizations. If the occasional World War got caused as a byproduct, that was fine by them, as the chaos of war often makes for fat and happy times for Vampires.
With the coming of Gehenna, the Black Hand was revealed to truly be dedicated to serving the Antediluvians who had founded the clans of the Camarilla. With the Antediluvians awake and once more in control of their clans, the Black Hand defected from the Sabbat, taking many of their best fighters and deepest secrets with them, and the Black Hand and Camarilla effectively merged in unified opposition to the Sabbat.
When most vampires were driven from Earth at the founding of the Earth Federation, the Camarilla and Black Hand factions formed the Kingdom of Enoch and the Sabbat was forcred into hiding. When Ventrue was killed on Wilke's Star by Mordred and Arikel died in the Supernova of the Enoch system, the Black Hand suddenly found itself with no Antediluvians to serve. When the remaining systems of the Kingdom of Enoch were conquered by the Earth Federation shortly after the Vin Shriak wars, the Black Hand was driven into hiding as well.
Now that new antediluvians have emerged in the wake of the Ascension War, the Black Hand has begun to put itself back together around Malkav, while the Camarilla has rallied around Ennoia and her new alliance with the Sabbat. The Black Hand thus finds itself effectively at war with both the Sabbat and the Camarilla.