Many people consider healing a lame person a great miracle and raising a dead person back to life an even greater one. But the spiritual salvation of a lost sinner is greater than both of them. The Lord performed the first two miracles through Peter ( Acts 9:32-43), and now He did the third (ch10). [source][source][source]
"In a sense this scene is the book"s turning point, as from here the gospel will fan out in all directions to people across a vast array of geographical regions, something Paul"s three missionary journeys will underscore." [1][source]
The episode concerning Cornelius is obviously very important since there are three lengthy references to it in Acts (chs10 , 11 , and15). It deals with an important issue concerning the mission that the Lord gave His disciples. That issue is how the Christians should carry out that mission in view of the obstacle of Gentile uncleanness. Gentiles were ritually unclean and communicated ritual uncleanness to Jews, according to the Mosaic Law, mainly because they did not observe Jewish dietary distinctions ( Leviticus 11). This obstacle kept Jews and Gentiles separate in society. [source][source][source]
Luke stressed four things in this conversion story particularly. First, the Christians initially resisted the ideas of evangelizing Gentiles and accepting them into the church apart from any relationship to Judaism ( Acts 10:14; Acts 10:28; Acts 11:2-3; Acts 11:8). Second, God Himself led the way in Gentile evangelism and acceptance, and He showed His approval ( Acts 10:3; Acts 10:11-16; Acts 10:19-20; Acts 10:22 b, 30-33 , 44-46; Acts 11:5-10; Acts 11:13; Acts 11:15-17). Third, it was Peter, the leader of the Jerusalem apostles, whom God used to open the door of the church to Gentiles rather than Paul ( Acts 10:23; Acts 10:34-43; Acts 10:47-48; Acts 11:15-17). Fourth, the Jerusalem church accepted the conversion of Gentiles apart from their associating with Judaism because God had validated this in Cornelius" case ( Acts 11:18). [2][source]
"Although Paul is the primary agent in the mission to the Gentiles, Luke wishes to make it plain, not only that Peter was in full sympathy with his position, but that, as head of the Church, Peter was the first to give its official blessing to the admission of Gentiles as full and equal members of the New Israel [3] by his action in the case of a Roman centurion and his friends ..." [4][source]