The Church is described as having four essential features: one, holy, catholic, and apostolic (see CCC 811 and Lumen Gentium, art. 81). What are these four essential features, and what do they mean?
One: The Church is one because her founder is Christ himself: "There is one body and one Spirit, just as you were called to the one hope that belongs to your call, one Lord, one faith, one baptism, one God and Father of us all, who is above all and through all and in all" (Ephesians 4:5). In Christ, we are united by the bonds of unity: our profession of one faith, our common celebration of worship, and apostolic succession (see below for more information) (CCC, art. 815).
Holy: Because Christ alone is all-holy, and Christ is the head of the Church, the Church is therefore also holy. The Second Vatican Council document Lumen Gentium explains this idea well: "The Church on earth is endowed already with a sanctity that is real though imperfect" (art. 48). The Church here on earth is pilgrimaging toward heaven, where she will be made perfect. Therefore, while the Church possesses sanctity here on earth, for she has Christ as her head, she is still on a journey toward perfect sanctity, which will be found in Heaven.
Catholic: The word "catholic" means "universal" (see CCC, art. 830). The Church is universal in two ways. First, Christ is her head, such that his presence also indicates the presence of the Church. Second, the Church is universal in that she is meant to preach the Gospel to all nations: "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Hoy Spirit" (Matthew 28:19). Christ gave the universal command that all the members of his Body are meant to spread his Gospel throughout the world. Through her internal and external works, the Church reveals to the world the Gospel of Christ, which means that the Church reveals the new law of love.
Apostolic: The Church is apostolic because of the apostles. We can say she is apostolic in three ways: she remains built on the foundation of the apostles through apostolic succcession; through the Holy Spirit, she continues to pass on the faith; and she continue to be sanctified through the successors to the apostles, namely, the priests, the college of bishops, and the Pope as her head (see CCC, art. 857).