What is Ecclesiastical Court?

Legal Definition
An ecclesiastical court, also called court Christian or court spiritual, is any of certain courts having jurisdiction mainly in spiritual or religious matters. In the Middle Ages in many areas of Europe these courts had much wider powers than before the development of nation states. They were experts in interpreting Canon law, a basis of which was the Corpus Juris Civilis of Justinian which is considered the source of the civil law legal tradition.
-- Wikipedia
Legal Definition
English law. Courts held by the king's authority as supreme governor of the church, for matters which chiefly concern religion.

2. There are ten courts which may be ranged under this class. 1. The Archdeacon's Court. 2. The Consistory Court. 3. The Court of Arches. 4. The Court of Peculiars. 5. The Prerogative Court. 6. The Court of Delegates, which is the great court of appeals in all ecclesiastical causes. 7. The Court of Convocation. 8. The Court of Audience. 9. The Court of Faculties. 10. The Court of Commissioners of Review.
-- Bouviers Law Dictionary
Legal Definition
A system of courts in England, held by authority of the sovereign, and having jurisdiction over matters pertaining to the religion and rifual of the established church, and the rights, duties, and discipline of ecclesiastical persons as such. They are as follows: The archdeacon's court, consistory court, court of arches, court of peculiars, prerogative court, court of delegates, court of convocation, court of audience, court of faculties, and court of commissioners of review. See those several titles; and see 3 Bl. Comm. 64-68. Equitable Life Assur. Soc. v. Paterson, 41 Ga. 364, 5 Am. Rep. 535
-- Black's Law Dictionary
Legal Definition
English courts presided over by the clergy.
-- Ballentine's Law Dictionary