The Communion of Saints is the union of the blessed in Heaven, the faithful on earth and the holy souls in Purgatory. The saints are united in Christ's Mystical Body with Christ as their head. In 1 Corinthians 12:27 St. Paul says, "Now you are the body of Christ and members of member." In Colossians 1:18 St. Paul affirms, "[H]e is the head of the body, the Church."
The saints are called the Bride of Christ in Ephesians 5:28-30, which reads, "He that loves his wife, loves himself. ... as also Christ does the Church: because we are members of His body." The mystical spouse of Christ is composed of members found in three stages of perfection: the Church Triumphant in Heaven, the Church Militant on earth and the Church Suffering in Purgatory.
In Heaven the saints are crowned for their triumph over sin while on earth. They reflect God's radiance in Heaven to the degree they grew in virtue in their earthly life. Saintly people on earth are called militant, as they strive to love God and neighbor while battling sinful temptations from the world, the flesh and the devil. Saints in Purgatory, or the poor souls, willingly suffer in purification of unremitted guilt from venial sins and atonement for temporal punishment remaining from sins they committed on earth.
The three folds of the universal Church are in communion with one another as they profess the same doctrine, obey the same authority and spiritually assist one another. The Church Triumphant assists the faithful on earth and the poor souls in Purgatory by their prayers. The Church Militant honors the members of the Church Triumphant and strives to imitate their virtue. The faithful also assist the holy souls in Purgatory with prayers, fasting, good works, alms and indulgences. The holy souls, in return, can pray for the faithful on earth.
See how the Communion of Saints make up Christ's Mystical Body in season two of Majesty of the Faith—Mystical Body.