Dictionary.com defines the word "substitute" this way:
The substitutionary atonement refers to Jesus Christ dying as a substitute for sinners. The Scriptures teach that all men are sinners (Romans 3:9-18, 23). The penalty for our sinfulness is death. Romans 6:23 reads, “For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.”Scripture supports the premise that Jesus died as our Substitute, as you'll discover if you read the GotQuestions.org article for yourselves. I'd like to highlight just one of the Scriptures involved in this doctrine. I particularly like this two-verse passage because the second verse offers the practical implication of Christ dying the death that you and I deserve.
That verse teaches us several things. Without Christ, we are going to die and spend an eternity in hell as payment for our sins. Death in the Scriptures refers to a “separation.” Everyone will die, but some will live in heaven with the Lord for eternity, while others will live a life in hell for eternity. The death spoken of here refers to the life in hell. However, the second thing this verse teaches us is that eternal life is available through Jesus Christ. This is His substitutionary atonement.
24 He himself bore our sins in his body on the tree, that we might die to sin and live to righteousness. By his wounds you have been healed. 25 For you were straying like sheep, but have now returned to the Shepherd and Overseer of your souls. ~~1 Peter 2:24-25 (ESV)Of course, future blog posts, Lord willing, will fully explore Christ's claim on those who receive His salvation. But let me throw in the spoiler that truly redeemed people--people who enjoy His salvation because He took their place on the cross--naturally gravitate to Him and begin to live righteous, holy lives out of a desire to express gratitude. The very thought that Almighty God would become a Man for the very purpose of suffering the punishment as my Substitute certainly gives me the desire to put my life at His disposal. After all, I have first-hand knowledge (albeit limited) of what it means to be a substitute.