In Acts 10:34, 37-43, Peter preaches about Jesus as the anointed one who brought goodness and healing, emphasizing that God shows no partiality between Jews and Gentiles. He recounts Jesus' life, death, and resurrection, affirming that all who believe in Him can receive forgiveness of sins. Peter's speech highlights the inclusivity of Christianity, reinforced by the Holy Spirit's active presence among Gentiles, marking a pivotal moment in the early church.