The Communion of Saints
In brief
The communion of saints is the unbroken fellowship of all who are in Christ — the living and the departed together. Death does not cut a Christian off from the Body of Christ, so the saints in glory remain our brothers and sisters, and our intercessors. When Orthodox Christians ask the saints to pray for them, they are doing what Christians have always done with one another: asking a living member of the same family to pray.
One family, unbroken by death
When Christ answered the Sadducees, He appealed to the God who calls Himself the God of Abraham, Isaac, and Jacob, and drew the conclusion: "God is not the God of the dead, but of the living" (Matthew 22:32). Abraham is alive to God. If that was true before Pascha, how much more after Christ has trampled down death: those who die in Him do not fall out of His Body. The Church is one body in Christ, "and every one members one of another" (Romans 12:5) — and membership in that Body does not lapse at the grave.
That is why the Epistle to the Hebrews, after its long roll-call of the faithful departed, says we are "compassed about with so great a cloud of witnesses" (Hebrews 12:1). The saints are not distant spectators; they surround us. The Church does not divide into two churches, one on earth and one in heaven — it is one Church in two conditions, and the Body of Christ holds both. Every Divine Liturgy makes this visible: the Church on earth sings with the angels and commemorates the Theotokos and all the saints, because they are present at the same feast.
Why we ask the saints' prayers
The obvious question: why not just pray to God directly? The Orthodox answer is — we do, constantly; nothing in the Church's life replaces prayer to God. But Scripture also commands Christians to pray for one another, and promises that "the effectual fervent prayer of a righteous man availeth much" (James 5:16). If you would ask a devout friend to pray for you — and every Christian does — it is no different in kind to ask those who have finished the race and stand near Christ. In the Revelation, the prayers of the saints rise like incense before the throne of God (Revelation 8:3-4).
Asking the saints' prayers is not worship, and the Church has always policed that line with care (veneration-vs-worship-proskynesis-vs-latreia). The saints are not demigods and have no power of their own; their intercession is powerful because of their nearness to Christ, whose grace made them what they are. As St. John of Damascus taught, the saints are honored as friends of Christ and heirs of God. First among them the Church honors the Theotokos, whose prayers she asks in nearly every service — always with the same ending: it is her Son who saves.
How the communion is lived
For Orthodox Christians this doctrine is less a theory than a set of relationships. The faithful keep icons of the saints and greet them with veneration; they carry a patron saint's name and keep the saint's feast as a name day; they read the Lives of the Saints the way one reads letters from older members of the family who made it home.
And the communion runs in both directions across death. The Church on earth also prays for the departed (praying-for-the-dead), entrusting them to God's mercy, because love does not stop where breath does. The meeting point of all of it is the Eucharist: at every Liturgy the Church commemorates the living and the departed together before the one Chalice, and the whole family — on earth, in paradise, in every generation — is gathered at one table in Christ.