What does Acts 10:42 mean?

Cornelius, a Roman centurion, is a devout man, meaning a Gentile who faithfully worships the Jewish God but has not fully converted to Judaism. He is generous and prays continually (Acts 10:1–2). Several days before, an angel appeared to him and said, "Your prayers and your alms have ascended as a memorial before God" (Acts 10:4). Outward behavior and faith in God are not required to "earn" an invitation—however, Cornelius' actions have demonstrated that his is the kind of heart open to hearing the gospel of Jesus Christ.

Peter is explaining to Cornelius that Jesus of Nazareth is the judge who found Cornelius worthy. God came in the chosen human form of Jesus (John 5:22–27), and Jesus knows our hearts (John 2:23–25). Years later, Paul will say something similar to the philosophers in Athens: "The times of ignorance God overlooked, but now he commands all people everywhere to repent, because he has fixed a day on which he will judge the world in righteousness by a man whom he has appointed; and of this he has given assurance to all by raising him from the dead" (Acts 17:30–31).

Many of the Athenian philosophers will reject Paul's words because they don't believe the dead rise again. Peter is telling Cornelius and his guests that he and, apparently, some of the men he brought from Joppa witnessed Jesus alive after the crucifixion. Jesus then commissioned Peter and the other apostles to share this witness to whomever would listen—"in Jerusalem and in all Judea and Samaria, and to the end of the earth" (Acts 1:8). They are currently in Samaria, but considering the Gentile audience, Peter is reaching the end of the earth.