The pope has two roles in the Catholic Church. First, he is the Bishop of Rome, secondly, he holds what is called the "Petrine Office."
This means he holds a ministry that is founded on two specific docrines, first being his primacy over the whole church. While this does mean the Pope has supreme power over the Church, it is a power exercised in communion with the Bishops in a complex fashion that has changed and evolved over the centuries. Since the Second Vatican Council, the papal primacy means the Pope must act "Collegially" with the bishops. This is vague term whose definition has sparked a lot of controvercy, but basically means a communion of local churches who in turn comprise what is known as the Church universal through a co-responsibility between the pope and the bishops in decisionmaking, but with the Pope acting as its head. What is necessary to remember in this is that primacy is an act of service to the rest of the Church. The Church, in turn is not the hirearchy in Rome, but who are the people of God.
The other doctrine is of infallibility, which means teaching without error. This is a much mis-understood term. First off, the Pope can only make infallible statements on issues of faith and morals. Second, there are two ways in which a Pope can proclaim a teaching as infallible. The first is by pronouncemnt (called ex cathedra
, literally, "from the chair"). Such pronouncements must closely reflect the faith of the whole Church, meaning there must be assent from the whole Church discerned by close communcation between the Pope and the bishops. In the last 150 years, there have been only two such pronouncements, the most recent being in 1952 (I think...).
The second way in which infallibility is exercised is in Ecumenical council with the Pope at its head. An ecumentical council is a gathering of the Pope and the Bishops in conclave to jointly decide matters affecting the whole Church. The most recent council is the Second Vatican Council in 1962.
Are you confused yet? I'm studying this stuff and it makes my head spin...