The resurrection vindicated the life, teaching, and death of Jesus. If he had not been raised to life, he would have been shown to be a liar and a fraud leading others astray with his eschatological teachings. To then hope in him as Savior and Lord would be complete folly because any who did would be throwing their lives away to a man who cannot deliver what he promised–resurrection to new life after death.
He, however, is no liar or fraud, but he is the Lord of Heaven and Earth who, though he was slain, yet lives.
Jesus came to the earth as God in the flesh to take the sin and guilt of the entire world upon himself and subject them to death. Because he was the righteous one, his death on our behalf was a sufficient payment to free us from our debt caused by our participation in sin. When Jesus died, it may have seemed that in fact iniquity and death had overcome him, and his mission was thwarted. Death, however, could not hold him and because of his resurrection on the third day, we can say that he put the powers of sin and death to open shame on the cross, stripping them of their power.
In his substitutionary death and victorious resurrection, then, Christ recapitulates, or remakes, humanity into his own image. Adam was a man who lost unity with God, Jesus is a man united to God in the very nature of his person. Adam was the first ruler on the earth, Christ is exalted as king over all the earth to reign eternally. Adam was taken from the ground, Christ was raised from the ground after three days. Adam was a priest before God, Jesus is our Great High Priest forever. Through his life, death, and resurrection, Jesus remade humanity into what we were always meant to be.
Because Jesus was truly raised to new life after his crucifixion, our faith in him is not in vain. We can be certain that because he is our Lord, and he was raised first, that we will also be raised to new life after we die. If anyone trusts in Christ as the crucified and risen Lord, then truly she will not die. She will one day fall asleep for as long as the Lord waits for the completed number of sheep to come into his fold. Then, her old, corruptible body will be made new and she will rise to a new life of incorruptibility in the manner of her Lord Jesus. She will then be freed from any propensity to sin. No calamity will befall her. No anxiety will ever again rack her mind. No sickness will plague her. No death will ever harm her with its vicious sting. This was won for her by the resurrection of Christ.
He promised that he would be raised after three days, and he promised that all who trust in him shall not perish. He was raised, we shall not perish.