The short answer is: to give his life for the world. But what exactly does this mean?

Here’s a little story to help us understand: There once was a nobleman who had disobeyed his king. His home was taken away, and he was sent to a prison for the rest of his life. His wife went with him and they eventually had children. Now these children share in the man’s sentence and are not allowed to leave as long as their father is imprisoned there. Many years pass, and much of the family gives up hope of ever leaving. Then, one day, a nobleman of similar birth and equal rank presents himself to the king. He offers himself as a substitute for the first man – volunteering to serve his sentence – becoming what is called a “RANSOM” for the first man. 

The king graciously accepts the offer and the first nobleman is released and restored to his estate. Because he is now free, the family he had while in prison is also free. These children, who never had real freedom because they were born prisoners under their father's sentence, are now also redeemed. They leave the prison and inherit the restored estate of their father together with him.
The first man in the story was Adam, who disobeyed God, represented by the king. The second man who willingly offered his life for the first man was Jesus. The man’s children are us, since we all came from Adam, which means we all inherited the penalty for his sin: a prison house of death. 

The perfect man Jesus taking the perfect man Adam’s place satisfied God’s quality of perfect justice. With Adam’s death sentence ransomed, (or, canceled out), all of humankind will be raised from the grave in God’s kingdom – just like the children in the story being allowed to leave the prison.

This is what we mean when we say that Jesus gave his life for the world.

1 Timothy (2:5,6 RVIC) says it was “… Christ Jesus who gave himself a ransom for ALL.” The ransom is THE central theme of the Bible, so it's important that we study and understand it.

So, why did Jesus come to earth? To be a “ransom” for Adam, so that eventually, humankind will no longer be under the death penalty. In the future, every person who ever died will be brought back to life. At that time (because of Jesus’ sacrifice so long ago) humankind will be given a new opportunity for eternal life by changing their sinful ways and learning how to live righteously on a perfect earth in God’s future kingdom.

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