I've never completely understood the purpose as to why God required that the Israelite's should kill an animal in order for God to forgive them.
There were two main meanings to this. The first was as a symbol of Christ, whose blood makes it possible for everyone to have their sins forgiven. The second is as a sacrifice in the more traditional sense: willingly giving up something important and valuable. And when your animals are both your livelihood and the food on your family's table, giving the best of your flocks to the Lord (and the sacrifices were required to be the best, not just any old animal) is quite a sacrifice indeed! By the Law of Sacrifice, the Lord teaches us to have faith and trust in him instead of getting too attached to material possessions and trusting in them to bring us happiness and success in life.
Genesis 2: 15-24 and Genesis 3: 1-24 tells the story of our beginning; And simply stated: The woman snared by the dazzling of jewels which was Satan's appearance and her child like-mind could not properly understand, the words she heard; She taking it to her husband and by his own desire accepted the words of the fallen immortal son, Satan, he created to be a cunning persuader, a deceiver, and destroyer, for his work on the earth is to destroy all men who will not hear the truth in God's word. For their fate will be as his in the latter days to come. But the disobedience of having too much knowledge at one time is and remain harmful to us. Therefore innocent animals were killed by God to provide clothing and heat for our unprotected bodies. For in sin there is shame and eternal death; this, we their children have been trying to cover up our inborn shame, in the sight of God the only Living Son of the Father, in the day of our creation.