What does 1 Peter 1:3 mean?
Peter shows us an appropriate response to God's great mercy to us: praise. Specifically, he blesses God the Father of our Lord Jesus Christ. God is one being, in three persons. Peter's letter will reveal some of the distinctions between Father, Son, and Holy Spirit. In this case, he praises the Father while acknowledging Christ as our Lord.Peter blesses God for His mercy. As we have seen already in verse 2, God has chosen us, sanctifies us, and gives us great purpose. All of this happens without our ever needing to earn any recognition from Him. This is "grace," which is when someone gives something positive the other person does not deserve. "Mercy" is when someone withholds a negative consequence another deserves.
Instead of the punishment we deserve, God gave us something we could never have purchased or earned: He caused us to be born again. This is the very thing Jesus told Nicodemus must happen for anyone to see the kingdom of God (John 3). Specifically, God caused us to be born again into a living hope, through the resurrection of Jesus from the dead.
It's one thing to hope we will be saved, to yearn for life after death. Jesus proved that this hope is not a fantasy. He died, then showed Himself alive to many witnesses. Our faith is not a wish for a better world. The reason for our hope in an eternity with the Father is that our Lord is alive. Because He lives, those who believe in Him will also be resurrected.
Bless God for His great mercy!