The Patriarchal Caste is a collection of Protoss tribe leaders, acting as leaders and statesmen of the Protoss as a whole. The other two Castes are the Templar Caste (the warriors) and the Khalai Caste (the workers).
With few exceptions, members of the Patriarchal Caste avoid fighting directly save for times of great need, as they are more concerned with leadership, religion, and organization. However, members of the Rhel'Kaeli Tribe form the High Council's guard.
Under the dictates of the Savra, each tribe has a definite proclivity or strength that adds to the Protoss as a whole. The dictates of the Savra advise a three caste system, which each tribe fit easily into.
The Patriarchal Caste reinstated Xel'Naga teachings and allowed all tribe leaders access to the archives, while other members of the tribes could observe copies of the original texts.
The Patriarchal Caste is controlled by the Patriarchal Assembly, which is in turn governed by a body called the High Council.