In Theocracy, a form of government, the institutions and people that govern the state are very close to the leaders of the main religion. If the religious leaders do not directly run some bodies of the state, they influence them very much. The word theocracy comes from two Greek words literally meaning God-government, and meaning the government is run by "The Church".
Modern-day states that resemble TheocraciesEdit
Iran is a theocratic republic. In Iran, two bodies, the Supreme Leader and Guardian Council consist of members who are not elected by the people. These two bodies are staffed by Shia clerics. The highest elected official is the President of Iran.
The Vatican City is a true theocracy, with no separation of church and state. The head of the Catholic Church is the leader of the country. The pope is elected by the Papal Conclave.  Most popes have stayed for the rest of their lives, but some have resigned. One who resigned was Pope Benedict XVI.
Many states have a state religion. Israel, for example mixes some aspects of rabbinical law and civil law. Also, the state hires rabbis. In some such states, religious leaders also have civil duties, not only religious ones.