The Spirit comes on the apostles as fire, enabling them to speak the Gospel of Christ and be heard in the native languages of the Jews gathered from around the Mediterranean for the feast of Pentecost. Peter again quotes Scripture, Joel 2, saying we are now in the last days. God has made Jesus Lord and Christ, proving it by raising Him from death, which David spoke of (Psalm 16). All must repent and be baptized in Christ, to receive forgiveness and the Spirit. This Gospel is for you, your children and those far off, meaning to Peter's audience, those back home. 3000 believe and are baptized. They continue as faithful Jews, in favor with the Jews, worshiping and praying in the temple, but also gathering in homes daily for teaching, fellowship, meals (Communion?), and providing for each other materially. Note the overlap of old and new covenants here. The defining outward characteristics of the Jew were his circumcision and temple worship. For the Christian they were his baptism and partaking of the Lord's Table. During this time in Acts, the Christians continue in their temple worship and don't repudiate their circumcision, but are also baptized and celebrate Communion.
Application: the core of the Gospel is given from verses 22-40. Have you spoken it to others recently? What do these verses say is the proof of its truth?