Anything ecclesiastical is related to the Christian church. An ecclesiastical office is the office at a church, and a nun’s habit is ecclesiastical dress. A hat with a propeller on top is not.
Ecclesiastical things have to do with Christian churches or the clergy. Pews, readings from the Bible, and stained glass windows are all part of the ecclesiastical world. The ecclesiastical hierarchy is the pecking order of the clergy, and high-ranking clergy are considered to be ecclesiastical authorities. Secular is the opposite of ecclesiastical.