The concept means a system in which the church is completely subordinate to the secular ruler, or conversely a system in which the ruler of the secular power is also the ruler of the church. The classic example is the Byzantine Empire under Emperors like Justinian. Another example would he the British monarchy, especially under the Tudors.

The concept was first defined as such in the 18th century by a German philosopher named Justus Henning Böhmer, but found its fullest treatment by Max Weber in his 1922 work Economy and Society.

Edit: To directly answer your question, it was not a specific ideology of rulers in the sense of communism, fascism, or democracy. No ruler ever said, "I'm a Caesaropapist".