The word for "Gehenna" in Greek is γεέννῃ(geennē). Jesus most likely used Gehenna as a symbol for the final eschatological judgment, i.e. the Second Death or Lake of Fire spoken of in Revelation 20. "Gehenna" is a transliteration of the Hebrew phrase "Ge-hinnom", which refers to the valley right outside Jerusalem. The valley is explicitly mentioned over 13 times in the OTHebrew Bible as either "the Valley of the Son of Hinnom"Ben-Hinnom"(Joshua 15:8; 18:16; 2 Kings 23:10; 2 Chronicles 28:3; 33:6; Jeremiah 7:31-32; 19:2; 6; 32:35), or "the Valley of Hinnom"(Nehemiah 11:30). And there are several allusions to the valley, the most prominent being Jeremiah 31:40 and Isaiah 66:24. We'll analyze substantial mentions of Ge-hinnom in the OTHebrew Bible.
But first, I want to clear up something up. It's a very popular notion that Gehenna refers to a perpetually burning garbage dump in the Valley of Hinnom. However, this notion has very little evidence to support it. See these articles here and here. So, what was Jesus talking about when He used "Gehenna"? For that, we have to go to the Hebrew Bible(that which Jesus was fully steeped in throughout His life).
In 2 Chronicles 28:3, we see that King Ahaz sacrificed his children in the fire in Ge-hinnom(c.f. 2 Kings 16:3). Manasseh, like his grandfather Ahaz, also burned his children in Ge-hinnom(2 Chronicles 33:6; c.f. 2 Kings 21:6). Jeremiah 32:35 tells us that "they built high places for Baal in the Valley of Ben Hinnom to sacrifice their sons and daughters to Molech," something the LordYahweh never commanded, nor did it enter His mind, that they should do such a detestable thing and so make Judah sin. Manasseh had "shed very much innocent blood, till he had filled Jerusalem from one end to another"(2 Kings 21:16). Because of this, Yahweh decided to bring massive calamity upon Jerusalem and Judah(2 Kings 21:12). When Josiah(Manasseh's grandson) took the throne, he reformed Judah(2 Kings 23:1-25). 2 Kings 23:10 says that Josiah "desecrated Topheth, which is in the Valley of the Son of Hinnom, that no one might burn his son or his daughter as an offering to Molech." We see that Tophet was the place of fire within the Valley of Ben-Hinnom where child sacrifices took place. Josiah made sureensured that no one would sacrifice their children in Gethe Valley of Ben-hinnomHinnom by totally wrecking it.
Already, we see that Ge-hinnom is a site of death and utter desolation, and due to the atrocities of human beings at that. It is because of these monstrositiesdepravities committed in the Valley of Hinnom that Yahweh decided to turn it against them and let Ge-hinnom serve as a place of the judgment that would be brought upon them by Him; the place where they once perpetrated horrific acts is now the place where God has brought heavy judgment upon them. This is seen plainly in Jeremiah, where Ge-hinnom is portrayed as a place where the apostate Israelites will be utterly eliminated by Yahweh.
All this certainly conjures imagesinvokes pictures of complete eradication and decimation. Ge-hinnom will be called the "Valley of Slaughter", filled to the brim with the corpses of those who have done vile and despicable things(i.e. burn their children alive in honour of false deities), rotting in oblivion and being decomposed by scavengers(birds of the sky and animals of the land); the intense language gives us the image of a bloody battle scene of utmost desolation, with no survivors and dead bodies laid out in the open. This same language with reference to Ge-hinnom is employed again in Jeremiah 19. Here are the highlights(but read the whole chapter);
Again, the images of death and destruction, with the dead bodies(carcasses)carcasses of the Israelites who were smitten by the sword of their enemies laid out in the open for scavengers to finish them off.
These images of death and destruction are the ones being conjured in the minds of Jesus' disciples when He employs Gehenna in His teachings. Ge-hinnom is nowhere associated with "spiritual death"(separation from the presence of God); only physical death(separation between body and life-breath/spirit). That Jesus would use Ge-hinnom, a place notorious in the Hebrew Bible for the brutal destruction of God's enemies, to signify a concept(i.e. eternal conscious existence separated from God) that is not only never once associated with Ge-hinnom in the Hebrew Bible but also completely opposed to the notions explicitly and incontrovertibly portrayed by Ge-hinnom is absurd, to say the least. That Jesus' disciples, entirely unfamiliar with the notion of eternal conscious separation(on account of the fact that such a notion is not explicitly[or even implicitly] found anywhere in the Hebrew Bible) and thoroughly acquainted with the notion of God slaying His enemies(especially with regard to Ge-hinnom, as seen by the foregoingaforementioned), would have ever believed such a thing, beyond absurd.3
The word used for "destroy" is ἀπόλλυμι(Strong's G622). I thoroughly analyze the word "ἀπόλλυμι" in my answer here. In short, ἀπόλλυμι never indisputably refers to "separating from the presence of God"(not that that would help ECT much, as I point out in my posts here and here), and when ἀπόλλυμι refers to "rendering unusable/useless", it's always with reference to inanimate, lifeless objects(there's no evidence it has such a usage with regards to living beings[e.g. humans]). But it's not like that matters anyway, as we will see. Jesus is clearly is making a contrast between the power/ability of God and the power/ability of men. Jesus is saying that what men CANNOT do, God CAN do; that is why He says, instead. He wants us to fear God instead of men because He(God) can do what they(men) cannot. What was it, again, that they could not do? Was it that men could not cause the ψυχή to be separated from the presence of God? Was it that they could not render it useless? Jesus said that men could not "kill"(that is, "render powerless and nonfunctional") the ψυχή(as they can with the body). So what Jesus is saying is that God has the capacity to render the life-breath totally inert, powerless, and inoperative, while men do not; hence we should fear Him rather than men. The right reading of this passage is this: What men can do to the body, but cannot do to the life-breath/spirit, God can do to both the body and life-breath/spirit in Gehenna, and hence we should fear Him rather than men. Men can cause the body to be entirely powerless/nonfunctional, but they cannot cause the life-breath to become powerless/nonfunctional; the life-breath returns to God, retaining all its life-giving properties, waiting until it can be reinserted into a person so as to restore them to life. In Gehenna, however, God can cause the life-breath to lose all its power and ability; to become entirely nonfunctional. Essentially, God can nullify/make void the vital life-breath in Gehenna, and(Gehenna signifying final eschatological judgment) He can do so with permanent(everlasting) effects. All this to say that God can cause the two components(body and life-breath) necessary to create a functional, animate being to become permanently nonfunctional(deprived of all their capabilities), making resurrection(which demands a functional body and life-breath/spirit) an impossibility in perpetuity, thereby rendering the person dead(and unconscious)34
for eternity. God can cause the everlasting "shut-down" of our existence, and accordingly, we fear Him. That is what Matthew 10:28 is saying!
3.
Here something to think about. If God genuinely hated sin, wouldn't He, oh I don't know, put an end to it someday? Guaranteeing that sin endures for eternity by resurrecting those who perpetrate it in immortal, incorruptible bodies doesn't seem like something a God who despises sin would do; it certainly sounds like something a God who relishes sin would do. Usually, when people hate something, the last thing they would want to do is deliberately ensure its eternal existence. Just a thought. ;)
4.
But why unconscious? Aren't the dead conscious? Sure, let's assume they are. People who believe in post-mortal death do so because they believe that the "conscious spirit" or "soul" lives on after death, correct? Well, if in Gehenna God causes the "conscious spirit/soul" to become inactive and nonfunctional, what is left with regards to being conscious? The whole reason there is consciousness after death is because the conscious spirit/soul lives on, remaining intact. But if God makes the spirit/soul void in Gehenna, how could those who are cast into Gehenna possibly be conscious? Both their body and their soul/spirit are entirely lifeless and inoperative, without the capacity to do anything, hence there is no room for any conscious experience(let alone the conscious experience of eternal torment).