God had commanded King Saul to destroy the Amalekites--everything and everyone, including the livestock. The purpose of this complete destruction was Israel's purity. If Israel did not destroy their enemies completely, they would be influenced by their enemies to disobey God, to their own destruction. Alas, King Saul did not obey God; the people took the best of the livestock.
Saul's rationale was that he did everything else right, and he was going to have the people use these animals they had taken to give sacrifices to the LORD.
The prophet Samuel's response was this:
"Has the LORD as great delight in burnt offerings and sacrifices, as in obeying the voice of the LORD? Behold, to obey is better than sacrifice, and to listen than the fat of rams." (1 Samuel 15:22)
The point God through Samuel was making was that obedience was better than sacrifices. The purpose of sacrifices was so that sinners could remain in good standing with God. When they sacrificed the animals, by God's mercy, they were able to appease the God against whom they sinned. But rather than receiving these sacrifices, God would have rather that they just obeyed Him to begin with.
We still have the propensity to do this. People think that if they do such and such a thing, it will make up for the sin they're unwilling to repent of. I once spoke with someone who was living in with his girlfriend, and he was convinced that he could make up for it by eventually being a good husband and father. God is uninterested in our making up for our sins with virtue. The good doesn't erase the bad.
Even Christians can do this. We can barter with God. "Well, I do do this, but I'll do this other thing to make up for it." God wants total obedience.
Not one of us could meet that standard. Every one of us has fallen short of God's perfect character and standard.
That's why Christ came and perfectly obeyed the voice of His Father. He perfectly listened to Him. He never needed burnt offerings and sacrifices, because He never sinned against God. This perfect life made Him the perfect candidate to be our substitute on the cross. He died on our behalf--as the ultimate sacrifice to whom all other sacrifices were pointing--so that all who believe in Him, rather than facing the wrath of God they deserve, will instead receive forgiveness and eternal glory.
Still, we who are saved ought not toy with God. We ought not to try to haggle with Him. With the Spirit in us, we should have the desire to perfectly obey Him out of grateful love.