What does Psalm 108:3 mean?

This is taken from Psalm 57:9, which David wrote while evading the murderous jealousy of King Saul (1 Samuel 19:1–2). The end of that psalm expressed David's intent to maintain his faith, despite danger. Psalm 108 combines the resolutions of Psalms 57 and 60, both expressing confidence in God and His supremacy.

God's primary relationship in the Old Testament was with the nation of Israel (Genesis 12:1–3; Exodus 19—24:8). However, this was meant to establish a "new covenant" (Jeremiah 31:31–40) which would eventually cover the entire world (Isaiah 49:1–6; Galatians 3:23–29). When David mentions "nations" and "peoples," he uses terms which Scripture typically applies to Gentiles. These are the non-Jewish persons of the entire world. After the resurrection of Jesus, Jews and Gentiles are united when they share faith in Christ (Romans 15:8–13; Ephesians 2:11–22). In the end times, the whole world will be joined in peace when Jesus rules the world in person (Revelation 20:4). Eternity will include people of all conceivable races and backgrounds (Revelation 7:9–10).