There are many ways that the Church is unified here on earth, but one of the principal avenues for unity is the reception of Holy Communion.
This is clearly evident in the name itself, which promotes a "common union."
Sacrament of unity
The Catechism of the Catholic Church dwells on this topic in its section on the Eucharist:
The unity of the Mystical Body: the Eucharist makes the Church. Those who receive the Eucharist are united more closely to Christ. Through it Christ unites them to all the faithful in one body -- the Church.
More specifically, Holy Communion strengthens the bond of unity that was introduced at Baptism:
Communion renews, strengthens, and deepens this incorporation into the Church, already achieved by Baptism. In Baptism we have been called to form but one body. The Eucharist fulfills this call: "The cup of blessing which we bless, is it not a participation in the blood of Christ? the bread which we break, is it not a participation in the body of Christ? Because there is one bread, we who are many are one body, for we all partake of the one bread."
St. Augustine also reflects on the unity of this sacrament in one of his sermons:
If you are the body and members of Christ, then it is your sacrament that is placed on the table of the Lord; it is your sacrament that you receive. To that which you are you respond "Amen" ("yes, it is true!") and by responding to it you assent to it. For you hear the words, "the Body of Christ" and respond "Amen." Be then a member of the Body of Christ that your Amen may be true.
He also exclaims in a sermon about the Eucharist, "O sacrament of devotion! O sign of unity! O bond of charity!"
Every time we receive Holy Communion, we are professing that we are in union with the whole Church, believing everything she teaches and promising to live a Gospel-centered life.
We may not always live-up to that reality, but that is why the Church gives us the sacrament of reconciliation, which reunites us to the Body of Christ and repairs any damage we may have done through our sins.
Holy Communion also prepares us for that day when we will be united for all eternity in the holy embrace of God.
