It means that the earth will be filled with Christians.
To see this, we need to go back to Genesis 1:26, where God gives his purpose in creating people:
Let us make man in our image, after our likeness. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth. (Genesis 1:26; see also vv. 27-28).
To be in the image of God means to reflect him and represent him. Reflecting God is at the essence of being in his image.
And reflecting God is the same thing as glorifying God. To glorify something means to make it look great (not, in this case, like a microscope, make something small look bigger than it is, but like a telescope — showing just how big something really is). So for God to say that he made us in his image is the same as to say that he made us to display his glory.
Further, when God gives dominion to humankind “over all the earth,” it shows that his purpose in creation was to fill the whole earth with his glory. That’s why God created humans — to fill the earth with his glory. This includes fellowship with him and one another, reflecting back to him the radiance of his worth in our character, actions, and delight in him.
Then the fall happened, and man sinned (Genesis 3). Theologians distinguish between the natural image of God and the moral image of God. We didn’t lose the natural image of God in the fall — for example, God reaffirms, after the fall, that man is in his image (Genesis 9:6). This is why all people still deserve to be treated with respect and dignity.
But we did lose the moral image of God. This means we stopped reflecting God’s moral attributes; we became corrupted and sinful, reflecting the opposite of what God is like. This is why Paul can say that, in Christ, we are being restored in the image of God (Colossians 3:10).
Here’s what this means: The mere expansion of the human race over the whole earth no longer fulfills God’s purpose in creation. It fills the earth with people in his natural image — possessing intellect, emotion, and will — but who are out of fellowship with God and ultimately against him (Genesis 6:5; Romans 3:10ff; etc.).
Yet, God prophesies that “the earth will be filled with the knowledge of the glory of the Lord, as the waters cover the sea” (Habakkuk 2:14 and elsewhere). In other words, God’s original purpose to fill the earth with his glory — his glory reflected through human beings — will be fulfilled.
But how can that be, since we have sinned and no longer reflect the character of God? This is what redemption accomplished. By dying for us, Christ secured not only the forgiveness of our sins, but also our sanctification (and ultimately glorification). Through Christ, we are made new and come to reflect the moral image of God once again (Romans 8:29). And, this is only through Christ (Romans 8:1-8; John 14:6).
Which means, therefore, that the promise that “the earth will be filled with the knowledge of the glory of the Lord, as the waters cover the sea” is a promise that the earth will be filled with Christians. It is a promise that God’s plan of redemption will be successful in bringing people to faith in Christ in every people group in the entire world.
Since it is through people reflecting the glory of God that God’s glory fills the earth (Genesis 1:26), and since we only truly reflect his glory through the redemption that Christ won for us and gives to us (Romans 2:28-30; Colossians 3:10), the promise that the earth will be filled with the knowledge of God’s glory is a promise that it will be filled with those who believe in Christ and glorify God in him.
One could even possibly say that it is a promise of the worldwide success of the gospel.
Or, it is at least an echo of that. One question could be: “does this promise refer to the new heavens and new earth, when all has been made new after Christ returns, or a time before he returns?” I don’t know for sure — I haven’t totally figured out the details of my eschatology! (Other than, of course, the most important things: Christ will return physically, the dead will be raised [believers and unbelievers], the final judgment will happen, and there will be a renewed heavens and earth for all the people of God.)
But we do know this: the gospel will reach all people groups before Christ returns (Matthew 24:14; Revelation 7:9-12). So it seems likely that the promise of Habakkuk 2:14 and related passage will have a type of fulfillment in this age, before Christ returns, and that the ultimate fulfillment will be in the new heavens and new earth.
So whether the main emphasis of the passage is on the new heavens and new earth or this age, the promise is clear: God will accomplish his original purpose of filling the earth with his glory. And this means that he will fill the earth with the gospel and those who have come to him through it, such that they are more and more being renewed in his image and displaying his glory in all of life.