Presbyterianism is presbyters working in presbyteries: elders working in elderships. While that generic definition would also cover the polity of other churches which trace their roots to the Genevan Reformation, the distinctive of Presbyterianism is the church court, the eldership, which is called Presbytery.
On the one hand, a Presbytery is described in terms of a geographical area and is made up of all the congregations of a denomination within the bounds of that area. On the other, a Presbytery is the eldership of the congregations within the bounds. It is made up of all the ministers within the bounds and a ruling elder from each congregation. If necessary, additional ruling elders are added to create a parity of ministers and elders.
Presbytery is the root court of the Presbyterian system. It determines the membership of General Assembly. It is responsible for the worship and discipline practiced and the doctrine preached within its bounds. It examines, licenses, ordains, and installs ministers; it holds their membership and disciplines them.
Interestingly, it took some time for Presbytery to emerge. At the time of the Scottish Reformation, there were the General Assembly, superintendents with their councils, and congregational elderships in larger towns. Smaller rural congregations without or with a limited number of elders looked to the last for advice. There was also, centred in that larger town, the prophesying or exercise. This was a weekly meeting of ministers and prospective candidates for the ministry together with ruling elders at which theological subjects were lectured on and discussed, sermons were preached and evaluated, and the gifts for the ministry tested.
By the 1580s, there remained the national General Assembly; however, superintendents with their councils had given way to regional synods and, there being more ministers and ruling elders, local elderships had developed. In urban areas where there was more than one congregation, there were Kirk-sessions which oversaw the congregation, and General Sessions which dealt with matters of common interest. In more rural areas, where elders were less plentiful, congregations were joined under one Kirk-session rather than referring concerns to the elders in the nearest large town. The exercise continued as it had done.
In 1592, the exercise became a church court: The Presbytery. It added to its functions of mentorship and continuing education those of transacting ecclesiastical business. The ambiguities of the 1580s were resolved, and the responsibilities of the elderships of that time divided between Presbytery and Session. Presbytery, with its key position and functions, was the radical, the root, court of the church. Sessions were committees of Presbytery, delegated to oversee congregational concerns.
It is fundamental to an understanding of Presbyterianism that the Scottish Reformers did not hold to the principle of the autonomy of the local church. They were profoundly connectionalist. They started off with a General Assembly. If there were not enough ministers for all the congregations, then congregations were to share. If there were no or not enough elders in a congregation, then there would be one eldership over a number of congregations. The elders of the congregations in a city would join in a General Session. These things belonged to the transitional days of reformation, but they are applications of the principles of Presbytery.
Although Presbytery is the radical court of the Presbyterian system, it took some time before there were enough Presbyters to bring it into being.