"who have been chosen according to the foreknowledge of God the Father, through the sanctifying work of the Spirit, for obedience to Jesus Christ and sprinkling by his blood: Grace and peace be yours in abundance." NIV translation
For those who deny the concept of the Trinity, (three parts of God), this verse should settle the issue. We clearly can see, here, that not only do they exist but how they function in our salvation. God the Father knew and chose us from the beginning of time to be His children.
For too long we, as Christians, have tried to water this down but the simple fact of the matter is that God, in His infinite wisdom, knew those that would accept His gift of grace and mercy even before the world was created.
He then sent the Spirit to call on our hearts and to set us apart (sanctify) us for Him. We see too that, after we are called by the Spirit and set apart, it is for obedience to Jesus. God has made Him Lord of all and that includes us as well. He shed His blood to purchase us and the "sprinkling by his blood" is a picture of salvation and holiness just as the blood was put on the doorposts of the Israelites while they were in Egypt to save their firstborn sons from the plague of death. Just as the sprinkling of blood was used in the Old Testament to cleanse and prepare things for God's use, He has done the same for us. The things that were sprinkled were never again to be used for anything but service to God and it is the same for us when we come to Christ.
The final part of the greeting is the granting of grace and peace in abundance. Grace is simply God giving us what we do not deserve and that is to have a close relationship with Him. Because of our sin, there was no way that we could draw close to Him on our own but He took care of that through Jesus Christ. Peace can only come through that right relationship with God. It does not matter whether it is an individual or a nation of millions of people, peace can only come through the Prince of Peace which is Jesus Christ and that peace is between us and God.
"Praise be to the God and Father of our Lord Jesus Christ! In his great mercy he has given us new birth into a living hope through the resurrection of Jesus Christ from the dead," NIV translation
The last verse looked at grace while here we look at mercy and they are closely linked. Grace was God giving us what we don't deserve where mercy is God NOT giving us what we deserve.
The result of both is the same as Peter goes on to say and that is our hope that we will be resurrected just as Jesus was and be with God forever.
As the opening to this verse says, the praise goes to God because it is simply from Him and not something that we have done. The praise comes from gratitude for what God has done for us!