Why Is the Catholic Church Unique?
"You are Peter, and upon this rock I will build my church" (Mt 16:18). When Jesus founded the Church, he established a concrete, visible institution that can be traced in an unbroken line down through the centuries. The Church is both a living organism and an organization. So Christian unity is expressed not only spiritually, but in organizational and practical terms as well.
When Jesus declared that the apostle Peter was the "rock" on which he would build his Church, he made it possible to identify that Church, to know where it could be found. St. Peter became the first bishop of Rome, and the bishops of Rome who have succeeded him (the popes) have continued to fill his special office as the "rock." The Church Jesus established is thus the Church in spiritual and organizational communion with the successors of St. Peter - the Catholic Church, which is also called the Roman Catholic Church because of the leadership role of the Church of Rome.
The central role of the Roman Church in historic Christianity can be seen in that Church's unique and decisive function in upholding Christian orthodoxy (literally, "correct doctrine") throughout the ages. It is also evident in the papal leadership in ecumenical councils (such as the Council of Trent and the Second Vatican Council).
Why is the Church called "Catholic"? The word means "universal." It describes both the scope of Jesus' saving mission - he came to redeem the whole world - and the extent of the organization he established - a global Church embracing all peoples. The first recorded use of the term is in a letter written by a bishop of Antioch, St. Ignatius, who was taught by the apostle John and may well have known the apostle Peter himself.
The Catholic Church, then, is the universal Christian family in communion with St. Peter's successor, the pope. Founded by Jesus Christ himself through the apostles, it is unique both in its catholicity and in its adherence to the "rock."