First, it is important we see this in its context: "But the heavens and the earth which now exist are kept in store by the same word, reserved for fire until the day of judgment and perdition [destruction] of ungodly men" (II Peter 3:7). This fire is the judgment of incorrigible sinners, the Lake of Fire, which is the second death (Revelation 20:14). In this unquenchable fire, likened by John the Baptist to being "baptize[d] . . . with fire," the unrepentant will completely burn up (Matthew 3:10-12).
Peter goes on to describe the effects of this unquenchable fire: ". . . in which the heavens will pass away with a great noise, and the elements will melt with fervent heat; both the earth and the works that are in it will be burned up" (II Peter 3:10). An unquenchable fire is one that cannot be put out. It burns until it has consumed all combustible material. Then it dies out for lack of anything else to consume. Everything will be burned up except for spirit beings, who are not affected by physical fire.
In verse 6, Peter uses the example of Noah's Flood as a type of the future cleansing of the earth by fire: ". . . by which the world that then existed perished, being flooded with water." Just as the earth continued to exist after the Flood, so it will continue to exist after the coming worldwide "Gehenna" fire (Matthew 5:29-30; 10:28).
Notice what Peter says in II Peter 3:13:"Nevertheless we, according to His promise, look for new heavens and a new earth in which righteousness dwells." In the book of Revelation, "a new heaven and a new earth" are mentioned immediately after the account of the Lake of Fire:
"Then Death and Hades [the grave] were cast into the Lake of Fire. This is the second death. And I saw a new heaven and a new earth, for the first heaven and the first earth had passed away [by fire]; and there was no more sea. And I, John, saw the holy city, New Jerusalem, coming down out of heaven from God. . . . 'Behold, the tabernacle [dwelling] of God is with men, and He will dwell with them [on the earth] . . ." (Revelation 20:14—21:3).
It is plain from this passage that the earth will still exist (Ecclesiastes 1:4).
The simple explanation of II Peter 3:10, then, is that the surface of the earth and everything physical on it, including the incorrigibly wicked, will be destroyed by an all-consuming fire. God will then renew the earth's surface (Psalm 104:30) and make it a pure, glorious habitation for Himself and the rest of the God Kingdom (Revelation 21-22).