From a Bible study found at Founder.org:
Peter and his group left Joppa and traveled north along the coastal road to Caesarea. If they went on foot, it must have taken them a good nine or ten hours, apart from stops. So it is the following day that they reached their destination. They found a considerable company awaiting them, for Cornelius was expecting them and had assembled not only his personal household but also his relatives and close friends. His spiritual humility and receptivity may be judged from the fact that, as Peter entered the house, he fell at his feet and worshiped him [25]. People often knelt before their superiors in the cultures of both the Old Testament and the Roman Empire. However, Christians disavowed such reverence because it was similar to the honor given a god. When there was a possibility of misunderstanding, Peter and others made their position clear [Acts 14:14-15; Revelation 19:10, 22:9].
If Cornelius’ act of falling down before Peter was unbecoming, so too according to Jewish tradition was Peter’s act of entering a Gentile home [28a]. But now Peter felt at liberty to break this traditional taboo and to enter Cornelius’ house, because God had shown him that no human being was unclean in his sight. Whether consciously or unconsciously, Peter had just now repudiated both extreme and opposite attitudes which human beings have sometimes adopted towards one another. He had come to see that it was entirely inappropriate either to worship somebody as if divine (which Cornelius had tried to do to him) or to reject somebody as if unclean (which he would previously have done to Cornelius). Peter refused both to be treated by Cornelius as if he were a god, and to treat Cornelius as if he were a dog. Peter went on to say that, having been sent for, he had come without even raising any objection [29].