“Let all the house of Israel therefore know for certain that God has made him both Lord and Christ, this Jesus whom you crucified.” (Acts 2:36 ESV)
Peter’s explanation of the miracles of Pentecost, particularly the speaking in tongues, gave him an opportunity to preach the gospel. This short sermon contains the basic facts of Jesus ministry, death and resurrection. These facts are enhanced by an appeal to the witness of the Old Testament Scriptures, in this case the prophet Joel and King David. Peter also cited the eyewitness testimony of the apostles and the testimony of the people who were there listening. These are some of the main elements that ought to make up a presentation of the gospel and these are contained in the Word of God as examples for us.
The important idea that Peter wanted to convey to those listeners was that now is the day of salvation, now is man made right with God. This is possible only by the death and resurrection of Jesus, the very man that the Jews condemned and rejected several weeks earlier. Peter lets them know that Jesus has risen from the dead and that He was no ordinary man, but He is Lord, that is Yahweh, as well as the promised Messiah.
In the ensuing verses Peter calls them to acknowledge their sins, that is repent and be baptized, which means openly declare their faith in Jesus. Then they will receive forgiveness and enter into the new life in the Kingdom of God filled by the promised Holy Spirit and in fellowship of the new community of God, the church.