The temple was a religious center. It was often the earthly home or point of communication with a particular god or goddess. Priests or priestesses in the temple acted as the servants of the resident god or goddess and managed contact to and from the people, plus instruction, rituals, petitions, and answers to questions. The most common form of petition was the prayer. Another was the provision of gifts that supported the temple and its servants. A less common petition was the sacrifice of animals or even humans. The general belief of the time was that the more elaborate a temple, the taller it was, and the more grand, the more disposed the god or goddess would be to provide good weather, rainfall, and crop yields, while keeping away pests, disease, and human invaders.
—Age of Empires manual
The Priest is actually available in the Stone Age (viewable through the Scenario Editor) despite the building itself not being available until the Bronze Age.