Presbyterian itself comes from Scripture the Greek word presbyteros meaning elder. Presbyterian indicates that we as individual churches and as a national denomination are governed by the elders.
The Christian Tradition of Presbyterians can be expressed in a somewhat simplified manner in the following words: Faith Alone, Grace alone, Scripture alone. Our Christian faith is in the God of creation as well as the God of Jesus Christ and focused on salvation through faith in Jesus Christ alone. Humanity is given salvation by the Grace of God alone-not through any human efforts. Scripture is the unique and authoritative witness to Jesus Christ and the God of creation who shows us love and offers us opportunities to serve and glorify God in our lives. Again this is oversimplified-but it is a place to begin understanding what we believe.
To help expand on these ideas some Presbyterians believe in Jesus Christ as head of the Church, that Christ calls the Church into being, Christ gives the Church its faith and life, and Christ is the Church's authority. Quoted from the Presbyterian Church USA Book of Order G-1.0000-1.0100.
The Presbyterian Church USA confesses the Scriptures to be the Word of God written, witnessing to God's self-revelation. Where that Word is read and proclaimed, Jesus Christ the Living Word is present by the inward witness of the Holy Spirit. For this reason the readings, hearing, preaching, and confessing of the Word are central to Christian Worship. Quoted from the Presbyterian Church USA Book of Order W-2.200.
For a more comprehensive understanding of the Presbyterian denomination please visit www.pcusa.org.