He reminds them how the all the prophets beginning with Samuel had predicted Jesus and the events surrounding him, indeed he said, even since the time of Abraham God had planned for this to happen when he told Abraham that all people on earth will be blessed by one of his offsprings (Gen22:18; 26:4). He also quotes from the Book of Deuteronomy where Moses says:
The Lord your God will raise up for you a prophet like me from among your own people; you must listen to everything he tells you. Anyone who does not listen to him will be completely cut off from their people (Deut. 18:15, 18).
As Peter does in every one of his speeches here he also takes the opportunity to invite his listeners to repent and turn to God for the forgiveness of their sins (3:19). We must remember that is how Jesus started his ministry on earth, by asking people to repent and believe the Good News (Mk 1:15). While this speech is shorter than the first one it has many similarities. Peter’s main goal in both of the speeches is to convince his audience that Jesus is the Messiah and therefore to repent and believe in