God, in this verse, sets out the two universal sides. The proud are on one side. Their deeds are not upright. On the other side are the just, those who live by faith. In a way, He is asking Habakkuk—and us, "Which side are you on? Can I count you among the proud, who will be destroyed, or the just, the faithful, who will be rewarded? Choose your side."
This verse is quoted three times in the New Testament, all by the apostle Paul. In Romans 1:16-17, he shows that the gospel Christ brought reveals God's righteousness, the way we are to live, which is by faith in Jesus Christ. Thus, he writes, "The just shall live by faith." It is a common misconception that the gospel is merely the announcement of the Kingdom of God. But it is much more than that: It is the instruction of God on how we are to live. It is the faith we must live. We are to live the gospel, the way Christ revealed in His life and teaching. We can live confidently according to God's Word because we trust God—we have faith in Him and His revelation.
A second quotation of this verse is Galatians 3:11, a usage slightly different: as a proof that God does not justify us by the law but by faith. To paraphrase, he says that God has granted us eternal life because of our faith in Christ not by our adherence to the law. The apostle makes this verse say, "The just shall have eternal life by faith, or because of faith"—our faith in Christ, and so we will live.
Finally, Paul quotes this verse in Hebrews 10:38-39: "Now the just shall live by faith; but if anyone draws back, My soul has no pleasure in him. But we are not of those who draw back to perdition [or to destruction], but of those who believe to the saving of the soul." Paul uses the quotation from Habakkuk much like Habakkuk himself does, showing the two sides of the issue: the just on the one hand, who go forward to reward, and on the other side the proud, those who draw back and are destroyed. If we desire to enter into His Kingdom and live eternally, we must believe God and live our lives accordingly. The proud draw back from God, and they receive destruction. If we live by faith, we go forward to perfection (Hebrews 6:1-2) and thus to salvation, not to destruction. Paul says in II Corinthians 5:7, "We walk by faith, not by sight." The lesson is, whatever the circumstances, we must obey God and let the chips fall where they may. We must always be faithful to be counted among the just.