What does Psalm 83:16 mean?

Asaph (Psalm 83:1) asks the Lord to humiliate and embarrass Israel's enemies (Psalm 83:4–8), in hopes they will turn to God. The idea of shame is mentioned again in the following verse (Psalm 83:17). A coalition of enemies seek to annihilate Israel, so Asaph prays for God to intervene (Psalm 83:1–3). That begins by remembering victories of Israel's past (Psalm 83:9–12). It has progressed to explicitly call for harsh judgment. Asaph evokes God's power demonstrated in His creation of nature (Psalm 83:13–15).

Pagan religions have many gods, but they are false deities which could never do what the true God, the God of Israel, can. Asaph wanted a display of God's power, through the forces of nature, to persuade the enemy nations to turn to Him. When the Assyrians laid siege to Jerusalem, King Hezekiah offered a similar prayer. He prayed, "So now, O LORD our God, save us from his [the Assyrian's] hand, that all the kingdoms of the earth may know that you alone are the LORD" (Isaiah 37:20).

Even though this is an "imprecatory" psalm, where the author calls for harm to come on someone else, Asaph's appeal is not out of control. Here, he speaks hopefully about the idea of these enemy nations turning towards God as they are convicted of sin. Of course, he fully expects that most will not do so (Psalm 83:17).