Presbyterian is simply a reference to our church’s form of government. There are three basic forms of church government: (1) hierarchical [e.g. Catholic, Episcopal, Methodist], (2) Congregational/Independent [e.g. Baptists] and (3) Presbyterian.
In Catholicism and Episcopalianism, the church is ruled by a hierarchy of bishops. In Catholicism the pope (Bishop of Rome) is the head of the church and authority flows from the top down.
In Congregational church governance the congregation is the final court of appeal.
In Presbyterianism the congregation is represented by the men it chooses to lead/shepherd them (Acts 14:23). The congregation then submits, in the Lord, to those they have chosen (Hebrews 13:17). The men whom the congregation chooses to shepherd them are accountable to a system of higher courts (presbytery and Synod; see Acts 15). These are two key principles of Presbyterianism: representation and accountability.
The leaders of a presbyterian congregation are called elders (see Acts 14:23; 20:17,28; Philippians 1:1; 1 Tim.4:14; 5:17; Titus 1:5; 1 Pet.5:1,2; James 5:14). In our denomination (Reformed Presbyterian Church of North America [RPCNA]), only men can serve as elders (1 Timothy 2:9-3:7).
Every congregation is composed of a plurality of elders and these elders form a Session. The Session oversees the members of the congregation. Two or more Sessions = a presbytery (1 Tim.4:14). Several presbyteries = a Synod or General Assembly (cf. Acts 15:1-31).
See also:
Reformed Presbyterianism Today by Pastor Edward Donnelly
History of the Reformed Presbyterian Church of North America by Dr. Wayne Spear
What is Presbyterianism? by Charles Hodge
Presbyterian church governance in Wikipedia
