Preaching Peace Through Jesus Christ
After declaring that God would accept anyone who feared Him and worked righteousness, Peter continued speaking:
"The word which God sent to the children of Israel, preaching peace through Jesus Christ--He is Lord of all--that word you know, which was proclaimed throughout all Judea, and began from Galilee after the baptism which John preached: how God anointed Jesus of Nazareth with the Holy Spirit and with power, who went about doing good and healing all who were oppressed by the devil, for God was with Him. And we are witnesses of all things which He did both in the land of the Jews and in Jerusalem, whom they killed by hanging on a tree. Him God raised up on the third day, and showed Him openly, not to all the people, but to witnesses chosen before by God, even to us who ate and drank with Him after He arose from the dead. And He commanded us to preach to the people, and to testify that it is He who was ordained by God to be Judge of the living and the dead. To Him all the prophets witness that through His name, whoever believes in Him will receive remission of sins" (Acts 10:36-43).

Peter taught that the word of God was sent to the Israelites by means of Jesus Christ, the One who is Lord of all (Lord of believers and unbelievers) and the One who makes peace possible for all (i.e., reconciliation with God). Cornelius and those gathered were familiar, to some degree, with Jesus and His teachings. Peter brings up key facts about the Lord that were important for his listeners to know:

The apostles were witnesses of these great truths. They believed them and taught them. They preached the gospel to the people, and now that even included Gentiles. How will Cornelius, his family, and friends respond to these words from Peter?