The following is an explanation of the doctrine of the penal substitution of Christ on the behalf of sinners. It comes from GotQuestions.org.
Question: “What is the doctrine of substitution?”
Substitution is one of the major themes of the Bible. God instituted the principle of substitution in the Garden of Eden when Adam and Eve sinned. By killing an animal to cover their nakedness (Genesis 3:21), God began to paint a picture of what it would take to bring mankind back into proper relationship with Him. He continued that theme with His chosen people Israel. By giving them the Law, God showed them His holiness and demonstrated their inability to achieve that holiness. God then granted them a substitute to pay the price for their sin, in the form of blood sacrifices (Exodus 29:41-42; 34:19; Numbers 29:2). By sacrificing an innocent animal according to God’s specifications, man could have his sins forgiven and enter the presence of God. The animal died in the sinner’s place, thereby allowing the sinner to go free, vindicated. Leviticus 16 tells of the scapegoat, upon which the elders of Israel would place their hands, symbolically transferring the sins of the people onto the goat. The goat was then set free into the wilderness, bearing the sins of the people far away.
The theme of substitution is found throughout the Old Testament as a precursor to the coming of Jesus Christ. The Passover feast conspicuously featured a substitute. In Exodus 12, God gives instruction to His people to prepare for the coming Angel of the Lord who would strike down the firstborn male of every family as a judgment upon Egypt. The only way to escape this plague was to take a perfect male lamb, kill it, and put the blood on the lintels and doorposts of their houses. God told them, “The blood will be a sign for you on the houses where you are; and when I see the blood, I will pass over you. No destructive plague will touch you when I strike Egypt” (Exodus 12:13). That Passover lamb was a substitute for every male firstborn who would accept it.
God carried that theme of substitution into the New Testament with the coming of Jesus. He had set the stage so that mankind would understand exactly what Jesus came to do. Second Corinthians 5:21 says, “He made Him who knew no sin to be sin on our behalf, so that we might become the righteousness of God in Him.” God’s perfect Lamb took the sins of the world upon Himself, laid down His life, and died in our place (John 1:19; 1 Peter 3:18). The only acceptable sacrifice for sin is a perfect offering. If we died for our own sins, it would not be sufficient payment. We are not perfect. Only Jesus, the perfect God-Man, fits the requirement, and He laid down His life for ours willingly (John 10:18). There was nothing we could do to save ourselves, so God did it for us. The Messianic prophecy of Isaiah 53 makes the substitutionary death of Christ abundantly clear: “He was pierced for our transgressions, he was crushed for our iniquities; the punishment that brought us peace was upon him, and by his wounds we are healed” (verse 5).
Jesus’ substitution for us was perfect, unlike the animal sacrifices of the Old Testament. Hebrews 10:4 says, “For it is impossible for the blood of bulls and goats to take away sins.” Someone might say, “You mean, all those sacrifices the Jews made were for nothing?” The writer is clarifying that animal blood itself had no value. It was what that blood symbolized that made the difference. The value of the ancient sacrifices was that the animal was a substitute for a human being’s sin and that it pointed forward to the ultimate sacrifice of Christ (Hebrews 9:22).
Some people make the mistake of thinking that, since Jesus died for the sins of the world, everyone will go to heaven one day. This is incorrect. The substitutionary death of Christ must be personally applied to each heart, in much the same way that the blood of the Passover had to be personally applied to the door (John 1:12; 3:16-18; Acts 2:38). Before we can become “the righteousness of God in Him,” we must exchange our old sin nature for His holy one. God offers the Substitute, but we must receive that Substitute personally by accepting Christ in faith (Ephesians 2:8-9).
Recommended Resources: Making Sense of Salvation by Wayne Grudem
Read more: http://www.gotquestions.org/doctrine-substitution.html#ixzz34QCruPS8