Holy Communion, by Angelo von Courten, late 19th Century
The Church understands the Communion Procession, in fact every procession in liturgy, as a sign of the Pilgrim Church, the body of those who believe in Christ, on their way to the Heavenly Jerusalem. All our lives we who believe in Christ are moving in time toward that moment when we will be taken by death from this world and enter into the joy of the Lord in the eternal kingdom He has prepared for us.
The liturgical assembly of the baptized that comes together for the celebration of the Eucharist is a witness to, a manifestation of, the Pilgrim Church. When we move in procession, particularly in the procession to receive the Body and Blood of Christ in Communion, we are a sign, a symbol of that Pilgrim Church "on the way."
For some, however, the experience of the Communion Procession is far more prosaic, analogous perhaps to standing in line in the supermarket or at the motor vehicle bureau. A perception such as this is a dreadfully inaccurate and impoverished understanding of what is a significant religious action.
The Communion Procession is an action of the Body of Christ. At Christ's invitation, extended by the priest acting in Christ's person: "Blessed are those called to the Supper of the Lamb" [Beati qui ad cenam Agni vocati sunt], the members of the community move forward to share in the sacred meal, to receive the Body and Blood of Christ which is the sign and the source of their unity.
In fact, each time we move forward together to receive the Body and Blood of the Lord, we join the countless ranks of all the baptized who have gone before us, our loved ones, the canonized and uncanonized saints throughout the ages, who at their time in history formed a part of this mighty stream of believers.
United States Conference of Catholic Bishops, The Reception of Holy Communion at Mass. Slightly reformatted to avoid a wall of text, bolded emphases added.