One big part of being Reformed is being Reformed in the area of church polity and practice. In other words, Reformed churches have a Presbyterian structure which is “re-formed” according to the New Testament model. Charles Hodge talked about this in his 1855 address called “What is Presbyterianism?” Here’s a nice summary paragraph from his speech:
The three great negations of Presbyterianism—that is, the three great errors which it denies are: 1) That all church power vests in the clergy. 2) That the apostolic office is perpetual. 3) That each individual Christian congregation is independent.
The affirmative statement of these principles is: 1) That the people have a right to a substantive part in the government of the Church. 2) That presbyters [elders], who minister in word and doctrine, are the highest government officers of the Church, and all belong to the same order. 3) That the outward and visible Church is, or should be, one, in the sense that a smaller part is subject to a larger, and a larger to the whole. It is not holding one of these principles that makes a man a Presbyterian, but his holding them all.
covenant presbyterian church (OPC)