Albert Barnes Commentary Psalms 94:1

"O Jehovah, thou God to whom vengeance belongeth, Thou God to whom vengeance belongeth, shine forth." — Psalms 94:1 (ASV)

O Lord God, to whom vengeance belongeth... - Margin, God of revenges. The idea is that it pertains to God to take vengeance, or to punish for crimes. See the notes at Romans 12:19. The appeal here is made to God in view of the crimes committed by others, and which are referred to in the subsequent part of the psalm. God is addressed as having the right to restrain and punish wicked people, and He is asked to interpose and assert that right in a case that clearly demanded it. The appeal is repeated to make it emphatic, or to denote “earnestness” in the petition.

Show thyself - Margin, as in Hebrew, “shine forth.” The meaning is, Manifest Yourself; come forth as such a God; prove Your right; display Your power, and show that You are a God opposed to crime and wrong. The same Hebrew word is used here that is found in Psalm 80:1, and that is there rendered shine forth. See the notes at that passage.