Presbyterian government runs through a series of courts, each made up of elders rather than a single office-holder. The session governs one congregation, consisting of its minister, called the teaching elder, sitting together with a number of ruling elders elected by the congregation; the session admits and disciplines members and directs the congregation's worship and affairs. Congregations within a region send ministers and ruling elders to a presbytery, which ordains and installs ministers, hears appeals from a session's decisions, and holds real authority over matters a purely congregational church would keep local. Presbyteries in turn send commissioners to a synod, and above that to a general assembly, the church's highest court, which interprets the constitution and sets denomination-wide policy.
The design is meant to sit between two alternatives Presbyterians reject: episcopacy, where a single bishop holds authority a congregation cannot appeal past, and pure congregationalism, where no outside body can correct a local church that has gone astray. A presbytery can discipline an erring minister or overrule a session in a way a congregationalist association cannot, while no single elder, minister or bishop in the system holds authority alone, since every court decides by the vote of elders meeting together.
This graded structure is what the tradition's name itself preserves, from the Greek presbyteros, elder, the office the whole system is built around.