He is going to punish the people of Amalek because their ancestors opposed the Israelites when they were coming from Egypt. 1
References for 1 Samuel 15:2
15.2 Ex 17.8-14; Dt 25.17-19.
Go and attack the Amalekites and completely destroy everything they have. Don't leave a thing; kill all the men, women, children, and babies; the cattle, sheep, camels, and donkeys."