In the Bible, redemption references freeing someone from bondage. Under Christian doctrine, Christ paid the ultimate price for the sins of mankind and bought mankind's redemption on the cross with his crucifixion.
One of the most cited examples of redemption in the Bible is the freedom bought for sinners. When a person sins, he or she becomes a slave to sinning. The death of Jesus Christ on the cross was the ransom for the sinner.
Once Jesus paid the ransom for sinners with his life, they were free. As a result, the newly free, or redeemed, is able to live freely. In addition to freedom, sinners also receive eternal life and are forgiven for their sins after Christ's death.