It is believed by many Jews that the Messiah will redeem them, unite them, and establish the Kingdom of God on Earth. Some Christians believe that this prophecy will be fulfilled in the second coming of Christ. How is that possible, when the Jews already rejected Christ as Messiah in the first coming? What is the Biblical basis of the belief that there is still a chance of Jesus fulfilling this Messianic prophecy in the second coming?
The idea is not that all Jews will be reconciled to God, but that a remnant will repent and return to the Lord in the last days. Paul explains it this way:
According to the NT writings the whole World has been redeemed by the death of Jesus, including Israel. The act is finished. This understanding about the redemption of all was explained by Origen c. 250.
Huffington Post May 23, 2013 "Pope Francis rocked some religious and atheist minds today (May 23, 2013) when he declared that everyone was redeemed through Jesus, including atheists."
Redemption is, of course, not the same as salvation.
Okay here is some additional explanation - it is only a quick answer. I ought to spend a week thinking it out properly.
In the NT, the Greek word for redemption means a releasing effected by payment of ransom 1a) redemption, deliverance 1b) liberation procured by the payment of a ransom
It is the price that the Redeemer paid for our release from the bondage of sin. With this payment the virtues that God withheld from the children of Adam, are now offered to all mankind. We have but to ask sincerely and deeply to receive these virtues. The two virtues are summarized as "holiness and justice." As Origen has explained, the absence of these virtues in the children of Adam, and his descendants, was like a stain on mankind. This stain is washed away by the incarnation and sacrifice of Jesus - we are "washed clean" by His blood. Redemption for us then, is a washing away of the stains that were "original sin" - a term used by the Church Fathers - St. Augustine and St. Thomas. Origen before them, and others Fathers.
This is my understanding, I am sure that a Priest or theologian could explain it better.
Salvation, on the other hand begins with a life centered on God, trusting in God, and loving God. Someone must show us how to repent, for this is to love God with all our heart mind body and soul. The Hebrew practice is Teshuva, a lifetime of improving our aim so we get closer to the mark - as Paul taught.
Jesus said: "be ye perfect, as your Father in Heaven is perfect."
Paul showed his followers how to realize The Christ within them. Jesus said to the twelve "the kingdom of God is within you."
Simply put: redemption is the price paid for the removal of the stains on us that had, until the crucifixion, prevented us from re-entering Paradise. Salvation is the process by which God makes us worthy to enter Paradise. (As the NT puts it: We must have on our wedding garments provided by God to enter the bridal chamber.)
This is a simple explanation of very complex theology, and you should do the research yourselves. My explanation is taken from Anglican Doctrine.