What does Psalm 83:13 mean?

This is one of the "imprecatory" psalms. To "imprecate" is to evoke a curse, or to wish harm. Asaph sees enemy nations conspiring to annihilate Israel (Psalm 83:4–8). In prior verses, he began asking God to repeat the harsh judgments which had fallen on enemies such as Midian (Psalm 83:9–12). Now, he turns to more direct language. Asaph calls for specific forms of harm to fall on these opponents. This passage is labeled an "imprecatory" psalm for that reason.

Both dust and chaff are worthless; the implication is that Israel's enemies were worthless in terms of morals and decency. Possibly the word "dust" refers to rolling things like dry weeds without roots. The wind picks them up and blows them over wide, open spaces. The imagery resembles rolling tumbleweed over the plains in Western United States. The tumbleweed serves no purpose useful to humans, and Israel's enemies served no good purpose.

Prior to modern machinery, farmers would gather grain from their fields and thresh it: striking it to separate different parts. The resulting mix was then tossed into the wind. The grain was heavy, and fell to the ground, while the inedible bits called chaff blew away in the wind. Psalm 1 describes the blessed man as fruitful, but also says, "The wicked are not so, but are like chaff that the wind drives away" (Psalm 1:4).