God commands total destruction of Amalek, of their people, livestock, etc. (v. 3)
Saul is given the task of executing a long-standing covenant verdict (Exodus 17:14).
The command against Amalek is not arbitrary, but rather it fulfills the judgment God had sworn.
Saul obeys partially, destroying what is "despised and worthless" while keeping Agag and the best livestock (vv. 8–9).
He has edited God's command according to his own judgment of what is worth keeping.
This is the same pattern as chapter 13, where Saul's own reasoning has been substituted for obedience.
God's word to Samuel is grief before it is verdict: "I regret that I made Saul king, for he has turned back from following me" (v. 11).
Saul meets Samuel with self-congratulation: "I have performed the commandment of the Lord" (v. 13).
The sheep and oxen are lowing in the background as he says it (v. 14).
His defense is that the animals were spared for sacrifice, dressing his disobedience as worship.
Samuel's rebuke is the theological center of the chapter: "Behold, to obey is better than sacrifice, and to listen than the fat of rams." (v. 22).
Saul's rejection of the Lord will result in God's rejection of Saul as king (v. 23).
Saul's response reveals that he has been concerned with his standing before men, not his standing before God (v. 30).
Samuel completes the work that God had requested of Saul by hacking Agag to pieces (v. 33), then departs from Saul (v. 35).
Christ is the king after God's own heart that Samuel's verdict was reaching toward.
Where Saul substituted his judgment for God's command and dressed it in piety, Christ obeyed perfectly, offering the sacrifice that was found by his perfect obedience (Philippians 2:8).