The heart of Christianity is obtaining something we did not already have: a faith (1a). Surely this word means “to believe”, but it also encompasses a whole new way of life, that is walked by faith. But faith itself saves no one - our faith is not in our faith. It is in the righteousness of Another - and note the three titles - our God and Savior Jesus Christ (1b).
Jesus is God, all of God, yet not exhausting God - a member of the Trinity. God demands perfect righteousness, and yet this is a fallen world. So in this fallen state God substitutes this righteousness with faith - has so since Abraham (Genesis 15:6). But God does not trust in faith by itself either. He graciously, mercifully provides the very thing He demands from us, and the very thing our faith is to rest on - righteousness. This He did by giving us His Son, who took our sin upon himself, and imputed his unstained righteousness to all who believe.
Thus Jesus is Savior - he delivers us from death, with divine power (3). Thus he is the Christ - the Anointed One of God, promised long ago to Eve in the Garden (Genesis 3:15).
Thus he is the proof that God keeps His promises, in full. So Peter calls us to bank and build our lives upon them (4). They are precious and very great, because by them, we get God. The “to-do’s” of the rest of the chapter are all empowered by faith, faith in His promises.