The early Christians referred to all members of the community as “saints,” not necessarily because they achieved moral excellence, but because they were made “holy” by belonging to a “group” whose lives were connected in God. In this sense, community and communion are synonymous with church which in this context goes beyond a mere physical place of worship.
The Communion of Saints like the vine and the branches, connects all people in present time, with those who came before, and those who have yet to be... it’s eternal. Love is eternal. God is eternal. God is love. We share love with one another. We share God with one another.
Yet, when we think of Communion it’s only natural for us to think of the Eucharist, (Mark 14:12-16,22-26) the sharing of the Lord’s Supper with one another. When we celebrate the Eucharist we consume the love of God through the Body and Blood of Christ and by extension share that love with one another. In so doing, "I believe in the Communion of Saints" is manifest. We do this in memory of Him.
In this dynamic act of sharing the presence of the Trinity becomes real to us: Love in us is shared through us in His name, by the power of the Holy Spirit, in Jesus name, Amen. It's an expression of a dynamic, intimate relationship that includes us in the Communion of God and man.
It is more than just the line in a prayer.