"We judicators are eternally grateful that our hierarch has allowed us to serve Aiur once more. And yet, you Templar are still wary of our actions. Our desire to fight for our homeworld is equal to any other."
The Judicator Caste was a collection of protoss tribes, acting as leaders and statesmen of the protoss. The other two castes were the Templar Caste (the warriors) and the Khalai Caste (the workers).
The Judicators, descended from the first tribes to join the Khala at the end of the Aeon of Strife, were selected by Khas and his students to act as leaders. 
Before the outbreak of war with the zerg, the Judicators controlled protoss society for thousands of years, often through the use of subtle psionics.
With few exceptions, members of the Judicator Caste avoided fighting, as they were more concerned with leadership, religion, and organization. However, members of the Ara Tribe formed the Conclave's guard. In addition, during the Great War, Judicators crewed arbiter support vessels.
Before the advent of the Khala, each tribe had a definite proclivity or strength. The dictates of the Khala advised a three caste system, which each tribe fit easily into.
The Judicator Caste banned all xel'naga teachings but continued to allow the Shelak Tribe to access the archives.
During the Great War, the Judicator Caste condemned ExecutorTassadar for refusing to burn the terran worlds and consorting with the dark templar. Tassadar declared that for too long the Judicators had dictated the will of the templar, and a brief civil war broke between the Conclave and Tassadar's followers. However, with a rescue from Zeratul and his dark templar, the Judicators and the Conclave gave Tassadar a chance to destroy the Overmind on Aiur.
After the fall of the Overmind, the Conclave and much of the Judicator Caste was destroyed by the rampaging zerg. Many Judicators fled to Shakuras with the rest of the Khalai.
After the Brood War, the remaining judicators chose Artanis to represent the Hierarchy. The Judicator Caste was removed from the power structure of protoss society, but several Judicators remained, and were integrated into Daelaam society.
During the End War, arbiters were redeployed on the frontlines, with protoss of the Judicator Caste assigned to command of them. However, due to their past actions they were deeply distrusted by the Templar Caste, nonetheless the Judicators were committed to the Daelaam. The Judicator Caste ceased to exist by order of HierarchArtanis, as he dismantled the caste system during the conflict.
The Judicator Caste was controlled by the Judicator Assembly, which is in turn governed by a body called the Conclave. The Conclave were a group of elders, chosen for their wisdom, knowledge of the Khala and adherence to the rules. The Ara Tribe dominated the assembly and thus the Conclave.