Catholicism is the entirety of the beliefs and practices of the Western and Eastern Churches that are in full communion with the pope as the Bishop of Rome and successor of Saint Peter the Apostle, united as the Catholic Church.
The first known written use of "Catholic Church" appears in a letter by St.Ignatius of Antioch about A.D. 107 to the church of Smyrna, whose bishop, Polycarp, visited Ignatius during his journey to Rome as a prisoner: in his letter to Smyrna, Ignatius wrote, "Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church." (Letter to the Smyrnaeans, 8) His use of "Catholic Church" suggests that it was already in current use, for he sees no need to explain himself and uses the expression as one already known to his readers. It gives expression to St. Paul's teaching that all baptized in Christ are one body in Christ (Gal.3:28; Eph.4:3-6, 12-16). Dissenting groups breaking away from this universal unity were already known to the Apostles: in his letters Paul refers to the "Judaizers" (those requiring observance of the Jewish Law), and in his Book of Revelation St. John calls them "Nicolaitans". It is a small step for those faithful to the teaching of the Apostles to identify themselves as the Catholic Church ("the one Church everywhere"), and not to include those dissenting and breaking away from unity with her.
The term Catholic Christianity entered into Roman law by force of edict under the Roman Emperor Theodosius on February 27 AD 380 in the Theodosian Code XVI.i.2: "It is our desire that all the various nations which are subject to our clemency and moderation, should continue the profession of that religion which was delivered to the Romans by the divine Apostle Peter, as it has been preserved by faithful tradition and which is now professed by the Pontiff Damasus and by Peter, Bishop of Alexandria, a man of apostolic holiness. According to the apostolic teaching and the doctrine of the Gospel, let us believe in the one Deity of the Father, the Son, and the Holy Spirit, in equal majesty and in a holy Trinity. We authorize the followers of this law to assume the title Catholic Christians; but as for the others, since in our judgment they are foolish madmen, we decree that they shall be branded with the ignominious name of heretics, and shall not presume to give their conventicles the name of churches. They will suffer in the first place the chastisement of divine condemnation and the second the punishment of [as] our authority, in accordance with the will of heaven, shall decide to inflict."
[Extract of English translation from Henry Bettenson, ed., Documents of the Christian Church (London: Oxford University Press, 1943), p. 31, cited at Medieval Sourcebook: Theodosian Code XVI by Paul Halsall, Fordham University. Retrieved Jan 5, 2007. The full Latin text of the code is at IMPERATORIS THEODOSIANI CODEX Liber Decimus Sextus (170KB download), archived from George Mason University. Retrieved Jan 5, 2007.]