Peter, an apostle of Jesus Christ, to the strangers scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia, Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied. (1 Peter 1:1-2 KJV)
Peter authored this book and it is assumed Silvanus wrote it down (1 Peter 5:12). In reading this book it appears that Peter's audience are Christians who are being persecuted (1 Peter 4:12-14) for their faith. Whether they are scattered throughout the regions mentioned because of persecution or just because they lived throughout a wide area, I'm not sure.
Peter says these Christians are elect according to the foreknowledge of God. To help understand the meaning of this, see Acts 2:23:
Him, being delivered by the determinate counsel and foreknowledge of God, ye have taken, and by wicked hands have crucified and slain:
We can see that foreknowledge means more than God just looking ahead and acting in accordance with what He sees man will do, but rather it is God carrying out His predetermined planned.
We are elect by His predetermined plan and His foreknowledge. This shows that He is sovereign over all.
What are we elected to? Sanctification, obedience and to the sprinkling of the blood of Jesus. It is through His death, burial and resurrection that we are saved. We are saved to be sanctified and to obey Him.
It is through Him we have peace and grace to endure the trials that life brings to us.