Why did Cornelius fall down and try to worship Peter?
Cornelius fell down at Peter's feet because, though he was a good man who gave alms and prayed, he was still ignorant of the true God and did not understand that Peter was only a human being. Peter immediately corrected him, saying, "Stand up! I myself also am a man."
Les explains that when Cornelius met Peter, he fell down at his feet and worshipped him. This should give a good indication of how far from the truth Cornelius was. Earlier, Cornelius is described as a good man who gave alms and prayed to God, yet he was so ignorant of the true God that he tried to worship a mere human being. Peter took him up and said, "Stand up! I myself also am a man." Peter then went in and found many that were come together. The account contrasts Cornelius's ignorance with Peter's plain testimony that he was only a man.
And as Peter was coming in, Cornelius met him, and fell down at his feet, and worshipped him.