Redeem: compensate for the faults or bad aspects of something; gain or regain possession in exchange for payment. 

Before the birth of Jesus, the idea of redemption without cost to the person seeking redemption was unheard of. In order to atone for their sins, people would have to make a sacrifice for their unintentional sins (or, the High Priest would make a collective offering on Yom Kippur). But, these offerings had to happen over and over and over again. One offering would only atone for past wrongdoings, not the wrongdoings that were still to come.

With the dawn of redeeming grace.
The birth of Jesus brought forth a paradigm shift. The idea that grace is offered freely and willingly to atone for the sin of another was nonexistent. Not only to atone for the sins that had come, but even the sins that are still yet to be. He came to us purposefully. He came with intention. From the very beginning, his path was clear. Unheard of, but clear. His very existence pointed to the cross.

The people who walked in darkness have seen a great light. Isaiah 9:2
Surely he has borne our griefs and carried our sorrows, yet we esteemed him stricken,
smitten by God, and afflicted.
But he was pierced for our transgressions; he was crushed for our iniquities;
upon him was the chastisement that brought us peace, and with his wounds we are healed.
                  . . . and the Lord has laid on him the iniquity of us all. Isaiah 53:4-5, 6b