The Greek word here has, from what I can tell, roughly the same range of meanings as the English word "destroy" can mean. Some make the case that destroy means to utterly annhilate, to cause something to cease to exist entirely; which is where some come to believe in Annihilationism. I'm not convinced of this view.
2 Peter 3:6 speaks of the world being destroyed by water during the flood; and verse 7 says the heavens and the earth will, likewise, experience the same by fire. Yet there was not a total annihilation, an erasure from existence, of the world by the flood, nor does the coming destruction by fire indicate the total annihilation of material creation; indeed Paul in Romans 8 instead speaks of the coming redemption of all creation, even as the Prophet Isaiah had spoken of a new heavens and a new earth, which St. John of Patmos repeats in the Revelation, whereby God makes all creation new. So that such destruction is not total annihilation; the natural created order came still existed after the flood, and it still will exist after the coming fire--this destruction speaks of judgment, and indeed the end of something. The flood was the end of things as they had been before the flood; and through the coming Judgment there will come an end to the way of things as they are now, and by making all things new the former way of things will be gone.
I would argue that the eschatological language of destruction should be understood within this larger context of Judgment and the ending of this present age, which is reserved for fire. All the evil of this present age shall be burned up, even as St. Paul speaks of Christians whose works will be judged, and there will be those who are saved, but as though through fire (1 Corinthians 3:15). There is that which has its end in destruction, judgment, and fire; and there is that which shall exist for eternity in the good new creation of the Age to Come.
So what happens when a person is entirely tied to that which is to be destroyed? Well St. John in the Revelation offers us the vision and image of a lake of fire, which is called "the second death".
So that all certainly sounds like it could be total annihilation, perhaps in some sense; and yet we also see in Scripture that the experience of these things is not the total annihilation of a person's existence; but is somehow persistent. Second death is not the erasure from existence; but is somehow a continued existence.
Because Scripture does indicate some kind of continued existence for the wicked, such as where Jesus calls the fires of Gehenna "age-enduring fire" or "eternal fire" where "the worm does not die" it has led to many, most even, in the Church to reject annihilationist views, and that instead there is some kind of ongoing existence for the wicked. Now, what that ongoing existence is, or even if it is entirely correct to call it an existence at all (perhaps we could call it a kind of sub-existence) is not entirely clear.
In the same way that trying to conceive of the glories of the Age to Come is near impossible, "What no eye has seen, no ear has heard..." "We see but through a dim glass..."; so also we have bare any way to conceive of what this persistence in destruction, this second death, really means. But one this is certain, Scripture considers this outcome incredibly serious; something to be avoided with as much intensity as the good of the future world is to be longed for.
I think we should avoid being very dogmatic about such things. But I think we can reasonably say some things.
As someone who does not subscribe to Eternal Conscious Torment, Annihilationism, nor Universalism, I try to avoid being overly dogmatic about certain things. But I do believe that the language of destruction is eschatological, and is tied to the idea that this present age--with all its evil and suffering--has a definitive end; and such things having no place in the Age to Come also means that we, ourselves, are to be people of that future age, rather than this one. That is, is my life a life redeemed and made new--and being made new--by the grace of God, the power of the Spirit, and abiding in Christ; or is my life thoroughly grounded in the sin and evil of this present age--am I in Christ, and therefore partake of the life of Christ who has overcome death, destroyed hell, and who reigns from the heavens and who in the end shall unite heaven and earth together under His rule; or am I outside of Christ, outside of the city where there is no refuge.
If we are each akin to the prodigal son, do we remain living in the pig slop forever, or do we come into the open arms of a loving father who has a home prepared for us. What does it look like if the prodigal son never returned home?
-CryptoLutheran