Theocracy is government by God, or, alternatively, government by someone considered God's representative, such as the head of the church. Theocracies have been relatively rare in history, and the only known one with the first definition was Israel prior to it being a kingdom.
Examples of the second definition were Tibet under the Dalai Lama, the Papal States and Florence under Girolamo Savonarola. One modern example is the Vatican City. Iran has also been considered to be a theocracy.
A related concept is caesaropapism, where the church is subordinate to the state.