What does Psalm 83:18 mean?

This is one of the "imprecatory psalms" which pray for harsh, direct harm to come to Israel's enemies. Asaph prays this way because of a coalition of enemies seeking to erase Israel entirely (Psalm 83:4–8). He referred to historical examples where God brought justice crashing down on enemy nations (Psalm 83:9–12). He has also called for God's power to be expressed with the destructive forces of fire, wind, and water (Psalm 83:13–15).

Despite his obvious anger against these enemies, Asaph recognizes the proper purpose of such disasters: to convince wayward nations that God alone is Most High (Psalm 83:16). Asaph closes the prayer with that thought in mind. He wants God to bring these enemies so low that they will see their weakness and need. They will see they are nothing compared to how high and mighty the Lord is.

Today, even in cultures which profess to be "Christian," true believers comprise a minority. Many unbelievers stubbornly refuse to acknowledge the Lord's right to direct their lives. Some even deny His existence. They may persecute and even try to annihilate God's people. But someday at the name of Jesus every knee will bow, in heaven and on earth, and every tongue will confess that Jesus Christ is Lord, to the glory of God the Father (Philippians 2:10–11). Someday, Jesus will return to earth to reign. At that time, He will rule the nations with a rod of iron (Revelation 19:15) and "of the increase of his government and of peace there will be no end, on the throne of David and over his kingdom" (Isaiah 9:7).