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Piety is a social policy tree in Civilization V. In Brave New World, it is available at the start of the Ancient Era and includes the following policies:
Game Info
Piety increases the 
Faith Faith of empires.
Adopting Piety allows you to build Shrines and Temples in half the usual time. Unlocks building the Great Mosque of Djenne.
Adopting all Policies in the Piety tree causes a Great Prophet to appear and Holy Sites provide +3 
Culture Culture.
Civilopedia entry
Piety means the devotion to a specific religion or spiritual belief system. A "pious" person is generally considered to be (literally) "holier than thou," closely following his or her religion's practices and accepting most or all of its tenets without question.