The absolute removal of evil from the world requires uprooting not just the wrongdoers, but their entire legacy. The ultimate downfall of the wicked involves the complete eradication of their children and descendants [ביאור שטיינזלץ, מצודת דוד]. The repeated focus on offspring emphasizes a final, uncompromising goal. It envisions a destruction so thorough that absolutely no memory or trace of the wicked will survive in the world [רד״ק, מצודת דוד, מאירי].
When identifying the targets of this destruction, some view it as a prayer directed to God, asking Him to wipe out the lineage of the wicked nation of Amalek [רש״י]. However, the phrasing of the action points to another possibility. Because the destruction is framed as something "you" will personally execute, some conclude that the address is not directed toward God at all. Instead, it is spoken to King David or the future Messianic King, marking the royal leader as the one who will actively defeat and eliminate these enemies [אבן עזרא].
A distinct perspective suggests that the descriptions of the descendants do not merely repeat the same idea for emphasis. Instead, they distinguish between different groups of children who did not actively participate in their fathers' evil actions. One group consists of the older children. Their sudden removal from the earth is a decree meant to spare them from the prolonged, agonizing disasters that fell upon their fathers. The other group consists of the younger children, who also perish in the same swift and immediate manner to avoid ongoing suffering [אלשיך].