A Kolinahr master is a respected position within Vulcan society that was formed after Surak's preaching of logic to his people. It is a religious rank that is somewhat similar to the role of a monk.
Young Vulcans journey to these Vulcan masters in order to learn the way of Cthia on how to suppress the burning emotions they contain which is achieved through the Kolinahr discipline. It takes many years after which the student awaits the masters to preside over whether they have completed their journey. (TOS movie: Star Trek: The Motion Picture)
One of the first Kolinahr masters, who was also a student of Surak, was T'Klass. (ENT episode: "Awakening")