What is Catholicism?
"...that which has been believed everywhere, always and by all. That is truly and properly 'catholic,' as is shown by the very force and meaning of the word, which comprehends everything almost universally."
S. VINCENT OF LERINS, IN HIS BOOK COMMONITORIUM [LINK]
When we talk about being Catholic, we are often talking about authority structures within the Christian religion. Many of us know that the Christian Church was erected as a development of the ancient People of God of the Old Testament, by a Jewish man called Jesus, who also declared himself openly to be the anointed king and successor to David, king of the Hebrew people, whose throne was in Jerusalem of the kingdom of Judah. This man, Jesus, called Christ (that is, the 'anointed one') also claimed to be the Son of almighty God and proved this with the things he said and did. Those who accepted his claims and became his followers were ordered in the manner of the ancient Hebrews into a church (a sacral gathering), with hierarchical 'elders' and priests, administering a new set of rituals for the sanctification of the people, acting as legitimate teachers and, above all, carefully directing the worship of God.
This structure persists within the episcopate of the Catholic Church, where bishops work together with the successor of the Apostle S. Peter to further the mission of Christ, until all people may be drawn into the Church and into union with Christ (Catechism of the Catholic Church, 857). It is because the Church is one and united in Christ, through the Apostolic tradition, that she can claim to be catholic; that she can claim to teach and live according to the will of her divine Master, the God-man Jesus Christ, who strengthens her with his own Holy Spirit and through the Sacraments that he instituted and entrusted to the keeping of the Apostles and their successors, the bishops of the Catholic communion.
So, what does it mean to be Catholic? It means that you and I, through our profession of a single Faith in its entirety, through the Sacraments of the Church, through her governmental structure and through Holy Communion - through all these things, we are members of a visible structure, under the rule of the Holy Father in Rome and the bishops in communion with him (CCC, 837). There are other Christians who have not professed the Faith in its entirety, and/or who lack communion with the Holy Father in Rome. This we call an 'imperfect communion,' for we still retain many links to these separated brothers and sisters of ours. Imperfect communion arrives in a variety of degrees and we of the Roman Catholic Church are said to be in so 'profound' a communion in particular with the Orthodox Churches of the Christian East as to even make possible a common celebration of the Eucharist (CCC, 838). The Catholic Church has prayed for Christian Unity from the very beginning, indeed since Christ himself prayed for it (Gospel of S. John, 17: 11-26), and would greatly rejoice when, God willing, all Christians are once more completely united, as their Lord desired.