To redeem is simply to buy back or recover ownership. To better understand this, if your car is impounded for unpaid tickets, you can get it back, or redeem it, by paying the fine. In this sense, Jesus redeems us from our imperfect state for God.
As such, Jesus acts as our redeemer, that is, one who redeems.
Redemption is the act of redeeming someone (see reconciliation).
A lifelong student of the Bible, Peter DeHaan, PhD, wrote the 700-page website ABibleADay.com to encourage people to explore the Bible. His main blog and numerous books urge Christians to push past the status quo and reconsider how they practice their faith in every area of their lives.