In the Epiclesis (or epiklesis), God's Holy Spirit is called on to come down "upon us and upon these gifts" (the bread and wine), so that they may become "truly the Body and Blood of our Lord and Savior Jesus Christ" . This is the main supplication in the Eucharistic Prayer.
The Orthodox Church believes, that the Holy Spirit is always "everywhere present and fills all things." The invocation of the Holy Spirit at the Divine Liturgy is the solemn affirmation that everything in life which is positive and good is accomplished by the Spirit of God.
During the Epiclesis, the people join their harts to the words and actions of the priest as he petitions God to make these gifts holy. The bread and wine offered in remembrance of Christ, are the gifts to be changed into the Body and Blood of Christ.
Again we offer unto Thee this reasonable and bloodless worship, and we ask Thee, and pray Thee, and supplicate Thee: Send down Thy Holy Spirit upon us and upon these gifts here offered.
And make this bread the precious Body of Thy Christ. (Amen)
And that which is in this cup, the precious Blood of Thy Christ. (Amen)
Making the change by the Holy Spirit. (Amen, Amen, Amen )
That these gifts may be to those who partake for the purification of soul, for remission of sins, for the communion of the Holy Spirit, for the fulfillment of the Kingdom of Heaven; for boldness towards Thee, and not for judgment or condemnation.
The entire work of God in making and saving the world is accomplished by the power of the Holy Spirit. He is the one who dwelt in Jesus making him the Christ. He is the one by whom Christ was incarnate of the Virgin Mary. He is the one who led Christ to the cross as the innocent Victim, the one who raised him from the dead as the triumphant victor.
The Epiklesis was a great dispute between Orthodox Church and other churches that needed to know how the change takes place and at what moment does it take place.
The Orthodox Church has always held the view that it is a mysterious reality, and that it is not within the power of our minds to apprehend it. It comes by the way of prayers. Not a moment of consecration. They look upon the entire Eucharistic Prayer as forming a single and indivisible whole, so that the three main sections of the prayer, Thanksgiving, Anamnesis, and Epiclesis, all form an integral part of the one act of consecration.
So, such a moment of consecration cannot come until the Amen of the Epiclesis.
Another dispute questioned if the prayer was necessary. So, at least in the Slavic tradition, the Prayer of the Third Hour was added to the epiklesis. It is a prayer asking the Lord to send the Holy Spirit to the Church right now as he did "at the third hour" to his holy apostles and disciples on Pentecost.