What does 1 Samuel 15:15 mean?
Saul, king of Israel, begins spinning excuses for his disobedience of the Lord. His approach will feel familiar to everyone who has ever tried to justify a wrong action after getting caught and being confronted. Saul's instructions were to destroy all animals of the Amalekites (1 Samuel 15:3). Samuel has asked how Saul can claim to be obedient when they can both hear the sounds of captured animals (1 Samuel 15:9). Saul strings together a series of justifications and deflections.First, Saul says "they" have brought the animals from the Amalekites. He draws the people into the situation as if it were not his fault alone. He will not even take responsibility for transporting the livestock to Gilgal. In a similar way, Saul says "the people" did not kill the best of the sheep and the oxen. Then he offers the excuse that they intended to use the captive animals for sacrifice to the Lord.
These are half-truths, at best. Saul did not personally drive the animals from Amalekite territory to Gilgal, and clearly the soldiers made their own choices (1 Samuel 15:9). It may even be possible that Saul planned to sacrifice some of the animals before the Lord. However, Saul was the king, and he was responsible to carry out God's command no matter what his soldiers wanted.
Next, Saul describes the Lord to Samuel as "the Lord your God." He doesn't express that this is "our" God or "my" God; his choice of words suggests that the Lord God of Israel isn't even his own God. This is another way of trying to remove himself from some of the responsibility for not doing what the Lord told Samuel to tell Saul to do.