One of the goals of the Westminster Assembly, commissioned by the English and Scottish governments, was to provide a "Form of Church Government" to unify the three kingdoms (England, Scotland, and Ireland). The divines were tasked with outlining a biblical form of government. The form that emerged was Presbyterianism. To be sure, there was opposition to this within the Assembly- the Independents wanted no system of government that looked anything like a hierarchy (they had enough of the Popish system) and the Erastians thought the civil government should carry out the discipline of the church and thus were not interested in granting jurisdiction to local churches, presbyteries and synods. But in the end, the Assembly voted, by a considerable margin, for a Presbyterian form of government. Very simply, Presbyterianism refers to governance by courts of elders. The elders of a local church are the first level of governance, called a Session today but referred to as a Presbytery in the 17th Century. The second court is made up of the elders from various regional local churches and is called Presbytery today but referred to as Synod in the 17th Century. The final court is made up of elders from the various national churches and is called General Assembly today (Synod in some Reformed churches) very similar to the 17th Century.
Alexander Mitchell, lecturing in the late 1800's on the Assembly's "Form of Government", wrote the following about the Presbyterian form of government-
Here is a superiority without tyranny, for no minister hath a papal or monarchical jurisdiction over his own flock, far less over other pastors and over the congregations of a large diocese. Here there is parity without confusion and disorder, for the pastors are in order before the elders, and the elders before the deacons. Every particular church is subordinate to the presbytery, the presbytery to the synod, and the synod to the national assembly. One pastor also hath priority of esteem before another for age, for zeal, for gifts, for his good deservings of the Church, each one honoring him whom God hath honored, and as he beareth the image of God, which was to be seen among the Apostles themselves. But none hath pre-eminence of title or power or jurisdiction above others; even as in nature one eye hath not power over another, only the head hath power over all, even as Christ over His church...
And lastly, here there is a subjection without slavery, for the people are subject to the pastors and assemblies, yet there is no assembly wherein every particular church hath not interest and power; nor is there anything done but they are, if not actually yet virtually, called to consent unto it.
Such is presbytery in theory, and there is no reason why in practice it should not approximate to the ideal more nearly than some recent caricaturists represent it to have done, save that we who are intrusted with its administration, not excluding these caricaturists themselves, still come far short of what we ought to be as men, as Christians, and as the descendants of such noble-hearted Christians; and that is a shortcoming that would mar any form of government which God has instituted, or human wisdom has devised.