The prophet Samuel reminds King Saul of the explicit and uncompromising mission placed upon him. God directed the king toward a clear, predefined goal, demanding the complete eradication of the Amalekites due to their wickedness. By sending Saul on this specific path, God established a distinct purpose, commanding him to entirely wipe out the enemy [מצודת דוד, ביאור שטיינזלץ]. To highlight the reason for this severe decree, the prophet specifically identifies the Amalekites as a people defined by their sin [ביאור שטיינזלץ].
The divine instruction required the army to wage war until the enemy was entirely consumed. The primary approach among commentators is that this directive focuses on the active duty of the Israelites carrying out the mission; they were expected to persist in battle until they had fully destroyed Amalek. Another perspective shifts the focus slightly, suggesting the emphasis of the command rests directly on the ultimate fate of the Amalekites, stressing that the war must not end until the enemy is entirely eradicated [רד״ק].