Before ascending to heaven, Jesus gave the Great Commission. He told His disciples "that repentance and remission of sins should be preached in His name to all nations, beginning at Jerusalem" (Luke 24:7 NKJV). He commanded: "Go into all the world and preach the gospel to every creature. He who believes and is baptized will be saved; but he who does not believe will be condemned" (Mark 16:15-16). Again Jesus said: "Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit" (Matt. 28:19).
In obedience to Jesus, the apostles began preaching the gospel in Jerusalem, but the gospel did not stay in Jerusalem. Peter told the Jews of Jerusalem: "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins" (Acts 2:38). He preached "repentance and remission of sins" to the Jews (Luke 24:7). However, the same gospel was not only for the Jews but for the Gentiles. The promise was "to all who are afar off" (Acts 2:39). While Peter did not know it at the time, he would be instrumental in the Gentiles obeying the gospel (Acts 10).
Cornelius was a centurion who lived in Caesarea. He was a prayerful man. He was a good man, but, like all men without the Lord, he was lost. An angel told Cornelius to send for Peter. The angel told Cornelius: "He will tell you what you must do" (Acts 10:6). He would tell the Gentiles what they needed to do to be "saved" (Acts 11:14).
Cornelius sent men to Peter at Joppa to summon him to Caesarea. In the meantime, Peter saw a vision. The Spirit instructed Peter to go with the men sent. When the men arrived, Peter lodged them. On the next day Peter went away with them to Caesarea. When Peter met him, Cornelius told him how the angel said to send for him. Cornelius said to Peter: "So I sent to you immediately, and you have done well to come. Now therefore, we are all present before God, to hear all the things commanded you by God" (Acts 10:33).
After hearing the testimony of Cornelius, Peter began to preach the "gospel" to the Gentiles (Acts 10:34-43; c.f. Acts 15:7). Peter introduced the sermon by saying: "In truth I perceive that God shows no partiality. But in every nation whoever fears Him and works righteousness is accepted by Him" (Acts 10:34-35). The gospel was for the Gentiles too! Peter taught the Gentiles about the ministry of Jesus. He preached the fundamental facts of the gospel: the death, burial, and resurrection. He testified that the resurrected Lord was seen by witnesses. Among other things, he also declared that Jesus would be Judge.
As Peter was preaching the gospel to the Gentiles, he said concerning Jesus: "To Him all the prophets witness that, through His name, whoever believes in Him will receive remission of sins" (Acts 10:43). Peter taught that baptism is "for the remission of sins" (Acts 2:38). The Gentiles could also be baptized for the remission of sins, but first Peter said that they needed to believe in Jesus. "While Peter was still speaking these words, the Holy Spirit fell upon all those who heard the word" (Acts 10:44).
Having heard the believing Gentiles miraculously speak with tongues and magnify God, Peter answered, "Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have" (Acts 10:47)? What did Peter tell the Gentiles that they must do to be saved? What were they commanded? "And he commanded them to be baptized in the name of the Lord" (Acts 10:48). Will you become a Christian today?