What is meant by a new heaven and new earth? I often hear people talking about going to heaven but it seems more like we are destined for a new earth..

From my understanding in John's revelation, the afterlife consists of a new heavens and a new earth, and we end up on the new earth, where God dwells.


  (Rev 21:1)  And I saw a new heaven and a new earth: for the first
  heaven and the first earth were passed away; and there was no more
  sea.
  
  (Rev 21:2)  And I John saw the holy city, new Jerusalem, coming down
  from God out of heaven, prepared as a bride adorned for her husband.
  
  (Rev 21:3)  And I heard a great voice out of heaven saying, Behold,
  the tabernacle of God is with men, and he will dwell with them, and
  they shall be his people, and God himself shall be with them, and be
  their God.


What did John mean when he said "new heaven" and "new earth" in this passage?
Because the Father is said to be in heaven, in the Lord's Prayer (Matthew 6:9) and elsewhere. And in John 14:2 Jesus says:


  In my Father's house are many mansions: if it were not so, I would have told you. I go to prepare a place for you.


Thus it is rather reasonably assumed that Jesus went to prepare us a place in heaven itself.

Also Matthew's constant use of the phrase "Kingdom of Heaven" plays a part in this, as probably does 1 Thess 4:17 "Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord."  

And because those who die before the New Jerusalem descends from the New Heaven to the New Earth in the book of Revelation, are probably in heaven in the meantime.  In Revelation itself, John places Christian martyrs in heaven by stating they are "under the altar" in heaven. (Revelation 6:9)  

Also, Jude 1:14 "...Behold, the Lord cometh with ten thousands of his saints,...."  but cometh from where?  2 Thess 1:7 "And to you who are troubled rest with us, when the Lord Jesus shall be revealed from heaven with his mighty angels,..."   So that would indicate these ten thousands of saints are with him in heaven prior to his second coming.