Presbyterian comes from a Greek word in the New Testament, presbuteros. It simply means “elder” and identifies how that congregation is governed.
The elders are of two types: 1) teaching elder or pastor; and 2) ruling elders (lay leaders). Both men and women who are spiritually mature in their biblical wisdom and who know and believe that Jesus Christ is their Lord and Savior can, if chosen by the congregation, serve as an elder.
So, in brief, the word Presbyterian doesn’t explain much more than how we are led under the authority of Christ and the teachings of the Bible.