Speaking in tongues, in the Bible, has two variations. It can mean, speaking with the languages of:
1-men, and
2-angels.
The first variation means that the Apostles learned many human languages by the power of the Holy Spirit, so that they could spread the gospel more effectively. This gift mostly died out by the third century. There is a late manifestation of it, however, in the story of St Ephraim of Syria, who miraculously learned to speak Greek, so he could converse with St Basil the Great of Caesaria.
The second variety, speaking with the tongues of angels, refers to what the Church Fathers call "prayer of the heart". This is the interpretation, for example, of St Niketas Stethatos (c 1005-1090). This refers to constant prayer; a result of illumination, which is the second stage of spiritual progress.
There are three stages to the Christian spiritual journey. The first is purification, or repentance. For the EO, repentance isn't just doing a good deed, like going to church after a long absence. Individual good deeds are just the beginning of the process of turning away from our passions, so that we're no longer interested in our old vices. It is this whole process which is purification/ repentance. At first we struggle to avoid temptations, to read the Bible, go to Church, fast, and pray. We struggle to keep our minds away from sin and on God, by reciting prayers silently, in our minds, day and night whenever we can. When God sees that we are ready for a deeper change in our hearts (our hidden, deeper selves) He sends His
grace to purify our hearts. Now we have reached true repentance. Our old vices don't attract us anymore. Anyone who expects to go to Heaven, must have reached at least this stage at the moment of death. Of course, this whole process can happen quickly, even in a single "jolt", if God wills it. This happened to some martyrs, who went from sinner to saint in a moment.
The second stage is illumination. It is possible, when one has reached the first stage, to fall back into sin. We don't believe in "once saved, always saved." Some others maintain their connection with God. When God sees fit, He sends them grace which illumines, or enlightens, them. Enlightenment, for the Fathers, doesn't mean 18th century atheism. It literally means to be "lit up" from within. Whereas we once had to force our attention on God, now we feel prayer welling up from out hearts. It becomes part of our nature, like breathing.
This is true constant prayer, 24 hours a day, when working or resting, when awake or asleep. Yes, even when we dream at night. It is called "prayer of the heart" because it is often accompanied by deep feelings of compunction, which we feel in the "bottom of our heart", literally the bottom of our chest. Sometimes, people in this stage are so overwhelmed by feelings of contrition, that they express them outwardly. They may lift their eyes and hands to heaven, sigh, groan, shed tears, fall on their knees, even lie prostrate on the ground. Such outward expressions can be misinterpreted by onlookers as drunkenness or insanity. It is also called "the tongues of angels" because angels are in constant communion with God, and they obviously don't make physical sounds with physical mouths.
The third and final stage is theosis, or divinization. A person in thte second stage can fall back into the first, or back into sin, by his own will. Those few who continue in the spiritual path, are granted by God to be able to commune directly with Him. This is theosis.
Through this gift, they can see God. This is "theoria". But what exactly do they see? We must make a distinction here, between God's essence and His energies. We have an essence which includes our flesh and soul. It is not made manifest when we interact with the world. One can't figure out our DNA by shaking hands with us, for example. God also has an essence - what He is within Himself. Neither we, nor the angels, nor any other created thing will ever know God's essence. It is forever unknowable and incommunicable to us. We also have energies; the way we interact with the world. They include our outward appearance, our voice, and our actions. God too has energies. They are ways in which God interacts with creation. In the OT they are the "hand of God", and in the NT "grace". In the western (RC and Protestant) churches, it is taught that God is in essence, simple. Therefore His essence and energies are the same thing, and are/is completely apart from creation. We EO say that this is presumptious. It assumes something about God's essence, which in reality is unknowable. The result is that Western theologians interpret the "hand of God" and "grace" as created things. We disagree. After all, it is not the "hand of creation" but the hand of God, and the grace of God. Those in theosis see God's grace as a "light" that permeates creation. People who die in this stage are called "Saint". They include the OT Patriarchs, the Prophets, the Apostles, and the Church Fathers.
No ancient Orthodox interpretation of speaking in tongues, has anything to to with the babbling carried out by modern Charismatics and Pentecostals. This bizarre practice is more akin to those of some ancient heretics, like the Montanists.