People were created to exist forever. We will either exist eternally separated from God by sin, or eternally with God through forgiveness and salvation. To be eternally separated from God is Hell. To be eternally in union with Him is eternal life. Heaven and Hell are real places of eternal existence.
"For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God's one and only Son."
"Now if we are children, then we are heirs, heirs of God and co-heirs with Christ, if indeed we share in his sufferings in order that we may also share in his glory. I consider that our present sufferings are not worth comparing with the glory that will be revealed in us."
1 Corinthians 2:7-9
"No, we speak of God's secret wisdom, a wisdom that has been hidden and that God destined for our glory before time began. None of the rulers of this age understood it, for if they had, they would not have crucified the Lord of glory. However, as it is written: "No eye has seen, no ear has heard, no mind has conceived what God has prepared for those who love him."
"Then I saw a great white throne and him who was seated on it. Earth and sky fled from his presence, and there was no place for them. And I saw the dead, great and small, standing before the throne, and books were opened. Another book was opened, which is the book of life. The dead were judged according to what they had done as recorded in the books. The sea gave up the dead that were in it, and death and Hades gave up the dead that were in them, and each person was judged according to what he had done. Then death and Hades were thrown into the lake of fire. The lake of fire is the second death. If anyone's name was not found written in the book of life, he was thrown into the lake of fire."