Can an Eastern Orthodox please answer this question?
Please bear with me, as this response will be rather lengthy—so lengthy that I’ll have to post it in two parts. Forgive me for being so verbose.
The essence-energies distinction is a very difficult concept of theology indeed, and I don’t think anybody can be faulted for finding it hard to understand. Indeed, I doubt most Orthodox laymen really understand it too well. That being said, as a humble layman myself, I shall try to explain it to the best of my abilities.
Firstly though, a bit of history. The essence-energies distinction was explicitly defined by Gregory Palamas in response to the Hesychasts Barlaam’s attacks upon Hesychasm. Hesychasm (a particular technique of prayer) might not have been so controversial in and of itself had it not been for one of its claimed side-effects: Hesychasts were said to experience in what they believed was the Divine and Uncreated Light—the same light which the apostles saw at the Transfiguration of Christ on Mount Tabor. This then brought up theological questions about the nature of the Uncreated Light at Tabor.
In response to Barlaam’s objections, Gregory Palamas formalized (or one could also say clarified) the essence-energies distinction. It is important to realize that Gregory Palamas did not invent the distinction, as the Cappadocian Fathers already spoke of and distinguished between essence and energies. Much in the same way that terms like “hypostasis”, “ousia” and “physis” (in English, person, essence and nature respectively) started off as vague theological terms which were later given precise meanings so that they were all clearly defined by the time of Chalcedon, so to did Gregory Palamas clarify the distinctions between two terms, essence (“ousia”) and energy (“energeia”), which were widely in use by the Cappadocian Fathers centuries before his time.
Barlaam, brought up in the Latin Scholastic tradition was scandalized by the idea of humans experiencing the uncreated. In defense of the possibility that mankind could have direct experience of the uncreated, Gregory Palamas distinguished between the Uncreated Essence (ousia) of God, which is unknowable, and the Uncreated Energies (energeies) of God, which are how God interacts with this world. We are invited to participate in the Uncreated Energies of God, both in this life and in the life of the age to come, but we are never invited to participate in the Uncreated Essence of God. The Essence of God is by definition unknowable for it is beyond our comprehension and beyond existence itself.
Thus, the essence-energies distinction answered several important theological questions which were brought up by the Hesychast controversy: if God is fully unknowable, then how does God make his presence known to us; how can we hope to achieve salvation if we cannot participate directly in God’s eternal energies; furthermore, although this is a bit of a rhetorical question, if the Light of Tabor was uncreated, how could the apostles have seen it if the uncreated energies of God are truly unknowable (would that not imply then that the source of the light of the Transfiguration was not divine)?
With the first question, we can see that the essence-energies distinction beautifully shows that part of God is unknowable, His Essence, but that he can make himself known to us through His Energies which are every bit as uncreated and divine as his essence. This also answers the second question as it is believed that our resurrection and eternal life in the age to come will be effected by the reestablishment of our connection to Uncreated Energies of God from which we were severed due to the original sin of Adam. This, by the way, is why Christ is called the second Adam: through the incarnation, a human body and soul were united with and made incorruptible by the Uncreated Energies of God, showing us what the true image of perfect humanity is. Some Orthodox even believe that hell is a consequence of the exposure of those who hate God to His Energy and His Love, for to them, they shall burn like fire.
The ultimate importance in the essence-energies distinction is that it protects Orthodoxy from the heresies which involve putting too much of a gulf between humanity and God, such as pantheism and deism. Only a theistic view of God is correct to us, for our God is neither just a manifestation of the universe as some Hindus would believe, nor is He merely an “initial cause” who after creating the universe becomes disinterested in His creation and moves on to better things—our God is the almighty creator who, despite his awesome power is intensely interested in what he has made; loves with great intensity each and every one of his creations; and manifests that interest through His Uncreated Energies, despite the fact that we can never come to know His Essence.
I hope that this has helped perhaps, although I fear that it might just cause more confusion. Like I said, the essence-energies distinction is a complex one, and I someday hope that I might have a better understanding of it like that of Gregory Palamas. It reflects the venerable tradition of mystical theology in the Eastern Orthodox Church whereby experience of God, not logic, is the only truly acceptable way to come to know Him, and this of course, can only be accomplished through fasting, prayer, and sincere devotion to God. We are all on a long journey to acquire the Holy Spirit, as Christians, and we must all pray that we shall some day arrive at that point.