The teaching I have heard is that after the end of the world, God will forgive everyone, even those in Hell and all will be reconciled or restored to Him. I believe this teaching was something Origen suggested or taught.
Answer
The Judgment of God at the end of the world is very clear (The Parable of the Sheep and the Goats - Matthew 25:31-46). The righteous will be separated from the unrepentent sinners forever. Hell is a real place prepared for the Devil and his angels where unrepentent sinners will go. We do not believe in a period of purification, i.e. Purgatory. Now is the time to reconcile ourselves with God wilingly because he cannot force us or override our free will.
With that said, the idea of a universal reconciliation is one which the Church leaves to the realm of mystery. She has not made any dogmatic declarations regarding its validity or otherwise. There are several Church Fathers who wrote about it, e.g. Origen, St. Gregory of Nyssa, and St. Isaak of Nineveh. For each of them, the thought that in the end, God would save everything and everyone, was born from their deep love for God and his goodness. To my knowledge, it was not something they proposed as doctrine, and therefore, it has not been accepted or denied as such.
St. Gregory of Nyssa, in particular, teaches that creation and all that is in it, is as of yet incomplete, since the fall of man disrupted the plan and path to deification and communion with God which had been set before Adam and Eve. Christ restores this path, through his own resurrected body, to which we are joined at Baptism, which gives us the potential to become saints, i.e. holy, sanctified, through a synergy of our repentance and God’s grace. This path to reconciliation with God commenced with Christ’s death and resurrection. This path to God finds its end, its fulfillment and perfection at the close of time with the second coming of Christ when God will be “all in all” (1Corinthians 15:26-27).
The notion of something finding its purpose and fulfillment is found frequently in the worship and spirituality of the Orthodox Church. For example, water finds its purpose and fulfillment in Baptism. Bread finds its purpose and fulfillment in the Holy Eucharist. A human being finds his true purpose and fulfillment in being a son and daughter of God. This is why Christ says, “The Kingdom of God is within you.” So, in this sense, the “reconciliation” has already begun on earth and will continue, as St. Paul says, “from glory to glory”(2 Corinthians 3:18).