Substitution means to take the place of something. Christ‘s death on the cross was substitutionary in that He took our punishment. Isaiah 53:4-6 says,

“Surely our griefs He Himself bore, and our sorrows He carried. Yet we ourselves esteemed Him stricken, smitten of God, and afflicted. 5 But He was pierced through for our transgressions.  He was crushed for our iniquities; The chastening for our well-being fell upon Him, and by His scourging we are healed. 6 All of us like sheep have gone astray. Each of us has turned to his own way. But the Lord has caused the iniquity of us all to fall on Him,” (Isaiah 53:4-6).

Our sin was imputed to Christ. That is, it was reckoned to His account so that when He died on the cross, He fulfilled the requirement of the law that states that the wages of sin is death (Romans 6:23).

Also, consider the following verses:

• “And He Himself bore our sins in His body on the cross, so that we might die to sin and live to righteousness; for by His wounds you were healed,” (1 Peter 2:24).
• “He made Him who knew no sin to be sin on our behalf so that we might become the righteousness of God in Him,” (2 Cor. 5:21).

The Lord Jesus died for sinners and on behalf of sinners so that we might be redeemed through the complete and finished work of Christ.

“There are two Greek prepositions that emphasize the substitutionary nature of Jesus’ death. The preposition anti, translated “for,” means Christ died “instead of” sinners (Matt. 20:28; Mark 10:45). The preposition huper, also translated “for,” means Christ died “in behalf of” or “in place of” sinners (Gal. 3:13; 1 Tim. 2:6; 2 Cor. 5:21; 1 Pet. 3:18). Philemon 13 shows that huper must mean “in place of.”¹Enns, Paul P., The Moody Handbook of Theology, p. 323.

Finally, the death of Christ was a legal act. Sin is breaking the law of God, and Christ’s substitutionary atonement was a satisfaction of the law of God.