The Church is One
Jesus established only one Church, not a collection of competing churches (Lutheran, Baptist, Anglican, and so on). The Bible says the Church is the bride of Christ (Eph. 5:23-32). Jesus can have but one spouse, and his spouse is the Catholic Church.
His Church also teaches just one set of doctrines, and those doctrines must be identical to the doctrines taught by the apostles. This is unity of belief.
Although some individual Catholics dissent from officially-taught doctrines, the authentic teaching authority of the Church—the pope and the bishops united with him—has never changed any doctrine. Over the centuries, as doctrines are examined more fully, the Church comes to understand them more deeply, but it never understands them to mean the opposite of what they once meant.
The Church is Holy
By his grace Jesus makes the Church holy, just as he is holy. This doesn't mean each member is always holy. Jesus said there would be both good and bad members in the Church (John 6:70), and not all the members would go to heaven (Matt. 25:31-46). But the Church itself is holy because it is the source of holiness and is the guardian of the special means of grace Jesus established, the sacraments.
The Church is Catholic
Jesus' Church is called catholic ("universal" in Greek) because it is his gift to all people. He told his apostles to go throughout the world and make disciples of "all nations" (Matt. 28:19-20).
For 2,000 years the Catholic Church has carried out this mission, preaching the good news that Christ died for all men and that he wants all of us to be members of his universal family (Gal. 3:28).
Today the Catholic Church is found in every country of the world and is still sending out missionaries to "make disciples of all nations" (Matt. 28:19).
The Church Jesus established was known by its most common title, "the Catholic Church," at least as early as the year 107, when Ignatius of Antioch used that title to describe the one Church Jesus founded. The title apparently was old in Ignatius's time, which means it may go back to the time of the apostles.
The Church is Apostolic
The Church Jesus founded is apostolic because he appointed the apostles to be the first leaders of the Church, and their successors were to be its future leaders. The apostles were the first bishops, and, since the first century, there has been an unbroken line of Catholic bishops faithfully handing on what the apostles taught the first Christians in Scripture and oral Tradition (Acts 1:15-26, 2 Tim. 2:2).
These beliefs include the bodily Resurrection of Jesus, the Real Presence of Jesus in the Eucharist, the sacrificial nature of the Mass, the forgiveness of sins through a priest, baptismal regeneration, the existence of purgatory, Mary's special role, and much else—even the doctrine of apostolic succession itself.
Early Christian writings prove the first Christians were thoroughly Catholic in belief and practice and looked to the successors of the apostles as their leaders. What these first Christians believed is still believed by the Catholic Church. No other church can make this claim.