Think of the whole of Christianity as a family tree. Presbyterians are a part of the branch called Reformed churches. These churches began in the 16th century during the Protestant Reformation. They looked to the teachings of John Calvin and Huldrych Zwingli as being reliable ways of understanding and interpreting the Bible. Reformed churches were so-called because they wanted to "reform" the Roman Catholic Church on the basis of the Word of God in scripture. Thus, Presbyterians are akin to Lutheran's in that we are Bible-centric Christians who trace our lineage back to the dawn of the Protestant Reformation.
Presbyterian Churches specifically get their name from their form of church government: government by "presbyters"...or elders. Each church is made up of members...those members nominate a group of elders (called a session) to lead the church. That group, or session, then nominates from amongst themselves a few to serve with other session members from neighboring churches. That group is known as "the presbytery". The presbytery likewise nominates a few to serve a larger group known as "the synod"...who of course nominates a few to serve the General Assembly. The General Assembly is the largest, most authoritative body within the Presbyterian Church, and meets relatively seldomly; generally convening to discuss potentially divisive matters of doctrinal importance.