Boyd’s Bible Dictionary:
(condemnation). Consignment to everlasting perdition (Matt. 23:33; Mark 3:29; John 5:29; 2 Peter 2:3).
Concise Bible Dictionary:
1. ἀπώλεια, “destruction” (2 Pet. 2:3).
2. κρίμα, “judgment, condemnation” (Matt. 23:14; Rom. 3:8; Rom. 13:2; 1 Cor. 11:29; 1 Tim. 5:12).
3. κρίσις, “judgment,” associated with eternity: “judgment of hell” (Matt. 23:33); “eternal judgment” (Mark 3:29) (where some Editors read “guilty of eternal sin”); and “resurrection of judgment” (John 5:29).
4. κρίνω, κατακρίνω, “judge, condemn” (Mark 16:16; Rom. 14:23; 2 Thess. 2:12).
From Anstey’s Doctrinal Definitions:
This refers to the judgment that belongs to those who are eternally lost (Matt. 25:46). They will exist in Hell eternally where they will pay the price for their sins. (See Hell.)
Some think that “everlasting destruction” (2 Thess. 1:9; Phil. 3:19; Matt. 7:13; 2 Peter 2:1, 12; 3:16, etc.) means that people are consumed by the fire of God’s judgment, and thus they cease to exist. This false doctrine is called Annihilationism. God’s Word indicates that “everlasting destruction” has not to do with the loss of a person’s being, but the loss of his eternal well-being.
It is clear from Job 14:22 and Job 30:24 that unbelievers still exist after they die. It says that they “cry” out and “mourn” even after they have been destroyed. Revelation 19:20 tells us that the Beast and the false prophet were cast alive into the lake of fire. Then, in chapter 20 we are told that the devil is put into the bottomless pit for the duration of the Millennium, and then let loose. And after a brief rebellion we read, “And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever” (Rev. 20:10). Note: the Beast and the false prophet were still there in the lake of fire after the thousand-year reign of Christ! They didn’t cease to exist. Again, it says in Revelation 14:11, “And he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb: and the smoke of their torment ascendeth up forever and ever: and they have no rest day or night.” Torment is a condition that requires a person existing to endure it. You cannot torment what does not exist. The Lord also said, “Their worm dieth not” (Mark 9:48). This indicates that the torments of a guilty conscience will not die in the lost under eternal punishment. Moreover, a number of Scriptures tell us that the fire of God’s judgment “never shall be quenched” (Matt. 3:12; Mark 9:43, 45; Luke 3:17). What need would there be for it to continue if those who are cast there are annihilated immediately? Some tell us that death itself is the judgment. But Scripture says, “It is appointed unto men once to die, but after this (death) the judgment” (Heb. 9:27). If “after” death is the judgment, how could death be the judgment?
Even in ordinary language “destruction” doesn’t mean the cessation of existence. For instance, if we took an axe and chopped a beautiful wooden table into pieces, we could be accused of destroying the table. Yet there would be just as much material lying in a useless heap on the floor as when it sat as a beautiful table. Once it has been destroyed, it can be no longer used for the purpose for which it was made—but the material out of which it was constructed still exists. It is the same with the destruction of human beings. Man was made for the glory of God (Isa. 43:21; Rev. 4:11); if he goes into “everlasting destruction,” he can no longer be fitted through salvation for the purpose for which he was created.