Revelation 21:1-8 tells us of the coming New Heavens and New Earth in order to remind us not to find our satisfaction in this world or to be overcome by this world and all that is in it because this world will one day be transformed. As a result of this renewal, God himself will inhabit this world in a way not seen before.
The relevance of this passage for believers is the idea of overcoming, stated in Rev. 21:7, where the Lord tells the reader that the blessings of the new creation are for those who overcome. Those who will inhabit this new creation and enjoy the blessing of God’s presence are those who endure to the end (Matt. 10:22; 24:13; 13:13) and thus who overcome as demonstrated in their faithful obedience.
This principle of overcoming was stated first in each of the letters to the seven churches (2:7, 11, 17, 26; 3:5, 12, 21). This passage marks the fulfillment of those the promises accompanying each call to overcome in the seven letters. Each of the promised blessings stated in those letters find their fulfillment in the new creation.