The Kuzunoha Clan is one of two assassination clans that existed in the country since ancient times, the other being the Azuma. The Kuzunoha are the main branch and the Azuma is a branch family. However, interactions between these two clans have almost died out.
The Kuzunohas specialize in shamanism. According to Nio, in practice, it is close to hypnotism and suggestions as members of this clan can take mental control of their target, steal their correct perceptions, and chase them to death, or make them kill others.
It's different from the Azuma clan that has always been connected through lineage, as the Kuzunohas have always been adopting people with abillities from the green class (successions from fencing schools and like).