Upvote:2
The "Communion of Saints", (stated in the Apostles Creed), in reading the passages in 1 Corinthians 12, seems to mean the sharing of those spiritual gifts afforded us from the Holy Spirit to strengthen and complete the body of believers who make up the church. Although God could create one individual who might possess all the spiritual gifts, our Father, through the Holy Spirit, designed the body to function using all the gifts independently through the saints to create an interdependence upon each other as we use these gifts. This incredible interdependence upon one another strengthens our body.
Upvote:4
Wikipedia has a good article on the concept. The phrase means that Christians are united in the Body of Christ, a teaching based on 1 Corinthians 12 (and some other passages).