2 Peter 3 contains a vivid image about how the heavens and earth will pass away and be burnt up. The focus of the chapter is to demonstrate the reality of it by using the great flood of Genesis as an example of how something similar has already happened. This is a useful reminder, but also the comparison can give some insight into the nature of this destruction and what the new earth will be like.
The motivation is all about the promised return of Jesus to the earth, and how the long wait for that would cause people to doubt whether he would be returning at all. Peter claims that it would be inevitable that these doubts would occur,
2 Peter 3:3: knowing this first, that in the last days mockers will come, walking after their own lusts, 4 and saying, "Where is the promise of his coming? For, from the day that the fathers fell asleep, all things continue as they were from the beginning of the creation." WEB
The Previous World
The explanation then follows that there was a previous heavens, and a previous world that had been created and then destroyed in the flood.
2 Peter 3:5: For this they willfully forget, that there were heavens from of old, and an earth formed out of water and amid water, by the word of God; 6 by which means the world that then was, being overflowed with water, perished. WEB
This is interesting because it shows that the earth as mentioned here is more than just the rocks and clay. It is as much about the people and society - which was what was destroyed in the flood. At the time of the return, we can see a similar destruction of the then present human society, though here it looks like the primary tool is fire rather than water.
In the prophecy of Zephaniah also talks of destruction of the surface of the earth.
Zephaniah 1:2: I will utterly sweep away everything off of the surface of the earth, says Yahweh. 3 I will sweep away man and animal. I will sweep away the birds of the sky, the fish of the sea, and the heaps of rubble with the wicked. I will cut off man from the surface of the earth, says Yahweh. WEB
The Sequence of Worlds
In addition, the way in which the earth is described as being created out of the water in 2 Peter, indicates that prior to the creation, the ball of rock we call the Earth was already there, covered in water. The creation process is then a formation of the world out of the planet that presumably already existed. So the “earth” is more an order of things, rather than the rocks and clay. One world was created and then destroyed in the flood. The assertion of Peter is that this second world will also be destroyed to make way for yet another.
2 Peter 3:13: But, according to his promise, we look for new heavens and a new earth, in which dwells righteousness. WEB
The interesting thing about the record in 2 Peter 3 is that it describes the unknown of the future in terms of the history that is recorded, to better understand the nature of the language. That way we can have a better idea of just what the new earth is to be. It's the same ball of rock, with a new world on it.