Peter preaches this to Cornelius, who has recently sent for him after “a man in a dazzling robe” stands before him and tells him that He has heard his prayers. Cornelius says to Peter, “You did the right thing in coming. So we are all present before God, to hear everything you are commanded by the Lord.” (Acts 10:30,33)
Peter begins by verbally recognizing that “God doesn’t show favoritism.” (Acts 10:34) Peter realizes that “in every nation the person who fears [God] and does righteousness is acceptable to Him.” (Acts 10:35) Peter then proceeds to tell Cornelius of the events which led to Jesus’ crucifixion and resurrection. Peter proclaims, “[Jesus] is the One appointed by God to be the Judge of the living and the dead.” (Acts 10:42)
If Jesus judges you as clean, then you are clean.
With Peter’s words, Cornelius and the other Gentiles with him, believe and through the Name of Jesus Christ each is saved from his sins. The Holy Spirit descends on each one so that they speak in other languages and declare the greatness of God. At this point, Peter calls for these new believers to be baptized with water for they have already been sealed by the Holy Spirit.
Seeking God and being sought by Him — in every nation, people are being saved. Even so, come Lord Jesus!