Jesus came so that He could be the sacrifice for our sins. His death on the cross was the atonement for the sins of mankind. Our sins were nailed to that cross with Jesus. So, why was the resurrection of Christ necessary? For one thing, if Jesus had died and remained in the grave, it would have been no different from any other man suffering that horrible form of death. Jesus was fully human, but He was also fully divine. His resurrection is proof that He was, in fact, the Son of God. So, in part, the resurrection was necessary because it proves to the world that He is who He said He is.
If Jesus had died and not risen, the atonement that we received through His sacrificial death would be no different from the atonement received through the sacrifice of a lamb. It would have been temporary and would have to be repeated every year, just as it had been since the days of Moses. But, because of His resurrection, the atonement that comes from His sacrifice was only required to be done once for all (Hebrews 7:27). That sacrifice is the source of eternal salvation for everyone who believes and obeys Him (Hebrews 5:9).
The resurrection was also necessary because it verifies the truth of Scripture. In Psalm 16:9-10, David spoke of the resurrection of the Messiah, who God had promised would descend from David's throne. In those verses, which Peter quoted on the day of Pentecost, David wrote that the Messiah would not be abandoned to the realm of the dead, nor would His body decay (Acts 2:30-31).
We believe that Jesus rose from the dead and we testify to that when we share our faith with others. If Jesus had not risen from the dead, then all that we believe, all that we testify to, and all that is preached in our churches would be useless and false (1 Corinthians 15:14-15). And, if Jesus was not raised from the dead, then our faith is futile, since we would still be in our sins (1 Corinthians 15:17). But, thanks to our loving and merciful God, Jesus did rise from the dead and His resurrection power gives us victory over sin and death! (1 Corinthians 15:56-57)