"The term 'Presbyterian' refers to the form of government that is used by a church or a group of churches. It derives its meaning from the Greek word 'presbuteros,' which is used throughout the New Testament in connection with the rule of the church, and is usually translated 'elder.' A Presbyterian church governs its congregation by both teaching elders (the pastor) and ruling elders (mature Christian men in the congregation gifted accordingly). Together they make up the 'Session' and join with 'Sessions' of other regional churches in their denonminaton forming a 'Presbytery.'
The role of the elders or session in each church is to promote and protect the purity and peace of its members. Its rule is of an ecclesiastical (pertaining to the church) and spiritual nature. Those ordained have been charged to watch diligently over the flock in their care by being a good and humble example, by teaching, exhorting, and encouraging the congregation with sound doctrine, by praying continually for its people, by visiting the sick, by administering the sacraments, by disciplining the disobedient and unrepentant, and by governing the worship service and church gatherings in a manner which reflects the love and care of Jesus Christ, the Good Shepherd.
Presbyterian churches find their roots in Scotland during the Reformation of the mid 1500's. John Knox, a disciple of John Calvin, helped reform the churches in Scotland to this form of government. Many other churches throughout Europe also reformed their church rule according to the model in the New Testament, though only the Scottish churches and some English churches used the name 'Presbyterian.'
Presbyterian church government is in contrast to two other forms of church government, Hierarchal and Congregational. The hierarchal form was and is seen most clearly in the Roman Catholic church, where there are many different ranks of office, each rank subordinate to a higher rank, and headed by the pope. Congregational churches, on the other hand, are separate and autonomous from each other in rule. Reformers believed that the sole head of the Church was Christ Himself, who works through offices which He has clearly instituted in His word, and not a single leader on earth. They also believed in maintaining a sense of unity and purpose with other churches, especially in matters of appeal and denominational policy."
From the Website of Christ Covenant Reformed Church, Columbus Ohio