We become members of the Church when we receive the Sacrament of Baptism. United with Christ's Death and Resurrection, we become parts of his mystical Body. An ordinary human body is animated and united by its spirit, and this is also true of the Body of Christ. Jesus sends his Holy Spirit to impart the divine life to the members of his Church and keep them in communion with each other. That's why St. Paul describes peace in the Church with these words:
I, then, a prisoner for the Lord, urge you to live in a manner worthy of the call you have received, with all humility and gentleness, with patience, bearing with one another through love, striving to preserve the unity of the spirit through the bond of peace: one body and one Spirit, as you were also called to the one hope of your call; one Lord, one faith, one baptism; one God and Father of all, who is over all and through all and in all.
— Ephesians 4:1-6
The metaphor of the body implies that the various members perform different functions that are mutually supportive. That's exactly where St. Paul goes with it in another of his epistles. It's worth quoting him at length to get a sense of how the image of the human body shows us how to live at peace with each other in the Church:
As a body is one though it has many parts, and all the parts of the body, though many, are one body, so also Christ... If a foot should say, “Because I am not a hand I do not belong to the body,” it does not for this reason belong any less to the body... If the whole body were an eye, where would the hearing be? If the whole body were hearing, where would the sense of smell be? But as it is, God placed the parts, each one of them, in the body as he intended. If they were all one part, where would the body be? But as it is, there are many parts, yet one body. The eye cannot say to the hand, “I do not need you,” nor again the head to the feet, “I do not need you"...
