"For Moses truly said to the fathers, 'The LORD your God will raise up for you a Prophet like me from your brethren, Him you shall hear in all things, whatever He says to you. And it shall be that every soul who will not hear that Prophet shall be utterly destroyed from among the people.' Yes, and all the prophets, from Samuel and those who follow, as many as have spoken have also foretold these days. You are sons of the prophets, and of the covenant which God made with our fathers, saying to Abraham, 'And in your seed all the families of the earth shall be blessed.' To you first, God, having raised up His Servant Jesus, sent Him to bless you, in turning away every one of you from your iniquities."
Peter had mentioned in 3:21 about "all things which God has spoken by the mouth of all His holy prophets." He then proceeded to quote from the great lawgiver and prophet of old, Moses, specifically from Deuteronomy 18:15-20. The Jewish people highly respected Moses and readily accepted the fact that he spoke by the authority of Almighty God. Thus, by quoting Moses, Peter was reminding his Jewish audience that if they wanted to please God, they were obligated to believe and obey what Moses said. So, what did Moses say in this passage?
Moses here predicted, under inspiration of the Holy Spirit, three primary points:
Does Jesus fit this description from Deuteronomy 18:15-20? Is Jesus the Prophet that Moses spoke of? The answer is a resounding "yes!" There is no question that Jesus came through the nation of Israel (cf. Matt. 1:1-17; Rom. 1:3). Jesus was indeed a Prophet like Moses in many ways. For example:
It would be difficult to find one who is more like Moses than Jesus of Nazareth (particularly in the last two points, which are most significant)! That being the case, the people were obligated to hear and obey Jesus! Tragically, however, instead of hearing and obeying this great Prophet, they killed Him! No doubt the audience is pained by their guilt as well as the threat of destruction since they are among those who refused to heed the Prophet like Moses! The preaching of the apostles certainly cut many to the heart, and, as was the case on Pentecost, many more would believe, repent, and be baptized as a result (cf. Acts 4:4).
In Acts 3:24, Peter states that Moses wasn't the only one who foretold of Christ. Many other prophets spoke and wrote of "these days" (i.e., the Christian age). The Israelites, being "sons of the prophets," should have listened to and obeyed the prophets. Furthermore, this was the case because of their relationship to Abraham (the father of the nation of Israel) and the promise God made to him. Peter is appealing to the highest possible authority in the mind of the Jews! God promised to bless all the world through the "Seed" of Abraham, which is Christ, ultimately (cf. Gen. 22:18; Gal. 3:16). Yet, the Jews rejected the very One God sent to bless them first! God had sent Jesus at the appropriate time (cf. Gal. 4:4) to bless and to save "in turning away every one of you from your iniquities" (Acts 3:26). Although they had slain the Christ, they could still be blessed by Him (and avoid the deserved punishment) if they turned from their wickedness and embraced righteousness (i.e., genuine conversion, which requires the individual to change both his mindset and behavior in hearing and obeying the message from the great Prophet Jesus; cf. 3:19).