What is Meant by The Promise of a New Heaven and a New Earth?

One passage in the Old Testament containing that promise is Isaiah 65:17, 66:22 "For, behold, I create new heavens and... a new earth: and the former shall not be remembered, nor come into mind." What sometimes is forgotten is that every passage has a context. Isaiah was a 7th century BC prophet. He began his ministry 740 B.C., and was projected into the future as apostle John was in Rev. 4–22. His work was just before the destruction of Judah by the Babylonians. Much of his book of 66 chapters has to do with the people's sin, which was the cause of the coming destruction.

In the New Testament Peter also refers to new heavens and a new earth: "But in keeping with his promise, we are looking forward to a new heaven and a new earth, The home of righteousness. 2 Pet. 3:13. Peter uses this expression, in a context referring to the second coming of Christ, to describe the final dwelling place of the righteous, which is heaven itself, as Jesus taught in John 14:1-4. Notice that the "new heavens and the new earth" are promised after the present heavens and earth have been destroyed 2 Pet. 3:10.
So the context, and the teaching of other passages, show that this term (new heavens and new earth) is a figurative expression for heaven itself. John 14:3

Another reference is that of Revelation 21:1: "And I saw a new heaven and a new earth, for the first heaven and the first earth had passed away, and there was no longer any sea.
The new heaven and new earth of Rev. 21:1 is the Holy City, the new Jerusalem the hope and expectation of all the saved.
It is the City whose foundations, whose builder and maker is God." Heb. 11:10, 13-16. Again, it is heaven itself which is being described.