What does Psalm 9:5 mean?

This establishes several of the great deeds (Psalm 9:1) for which David is giving thanks to God.

First, God "rebuked" these enemies of Israel. Built into the idea of a "rebuke" are concepts like correction, scolding, and reprimand. By thoroughly defeating these hostile nations (Psalm 9:3), the Lord strongly condemned their sins. He showed in a dramatic way that their aggression was wrong.

Second, God accomplished the physical destruction of these wicked armies. A drastic victory over invaders meant those forces would not survive to fight against Israel ever again.

Third, the Lord "blotted out their name forever and ever." Blotting is the act of removing a stain: covering over, dissolving, or erasing it from existence. Used in a biblical context, the phrase "blot out" typically means a total annihilation of a person, place, or nation. As with other such phrases, it assumes a level of deliberate exaggeration, to make a point about the thoroughness of destruction. For example, Exodus 17:14 records the Lord's words about Amalek after Joshua and his people defeated the Amalekites. The Lord said to Moses, "Write this as a memorial in a book and recite it in the ears of Joshua, that I will utterly blot out the memory of Amalek from under heaven." In his message to the Jews gathered at Solomon's portico, Peter urged them to repent and turn back to the Lord so their sins would be blotted out (Acts 3:19).