"Then [Peter] said to [Cornelius], 'You know how unlawful it is for a Jewish man to keep company with or go to one of another nation. But God has shown me that I should not call any man common or unclean. Therefore I came without objection as soon as I was sent for, I ask then, for what reason have you sent for me?' So Cornelius said, 'Four days ago I was fasting until this hour; and at the ninth hour I prayed in my house, and behold, a man stood before me in bright clothing, and said, 'Cornelius, your prayer has been heard, and your alms are remembered in the sight of God. Send therefore to Joppa and call Simon here, whose surname is Peter. He is lodging in the house of Simon, a tanner, by the sea. When he comes, he will speak to you. So I sent to you immediately, and you have done well to come. Now therefore, we are all present before God, to hear all the things commanded you by God" (Acts 10:28-33).
Peter begins by declaring that it was unlawful for a Jew to associate with a Gentile. Although the Law of Moses did not forbid casual interaction with Gentiles, the Jews had a long-standing custom of considering such unlawful. There was a middle wall of separation between the two, so to speak (cf. Eph. 2:14ff). The Jews viewed themselves as superior to all other peoples (non-Jews were considered to be "dogs" by them). Thus, the need for the vision from God. The creatures in the large sheet represented people! God wanted Peter to know that the Gentiles were not intrinsically unclean. Any uncleanness in them was due to personal sin, not race or genealogy. The Gentiles were worthy of the opportunity to hear the gospel! Peter does not quite have a full grasp on this last aspect yet (which is evident based on his question in 10:29). Peter came to Cornelius quickly and without objection because of God's vision and instructions to him, though he is still uncertain exactly why his presence was needed. Sometimes truth penetrates in stages.
Cornelius explains the events of the past several days and that it was a message from God that had ultimately summoned Peter to Caesarea in order to speak the words of life to these Gentiles. Cornelius had been told by the angel that Peter would tell him what he "must do" (10:6), and now Cornelius is ready to listen, learn, believe, and obey!
"Then Peter opened his mouth and said: 'In truth I perceive that God shows no partiality. But in every nation whoever fears Him and works righteousness is accepted by Him" (Acts 10:34,35).
Peter proclaimed that God is not partial (cf. Rom. 2:11; I Sam. 16:7). God does not judge as man judges. He is willing to accept anyone, regardless of gender, age, race, social status, etc., if two general conditions are met. God would accept anyone from any country who feared Him and worked righteousness. In other words, God will accept anyone who has a healthy respect and honor for Him and is willing to submit himself in obedience to God's commands (i.e., righteousness, cf. Psa. 119:172). The expression "works righteousness" is significant and conveys more than just the need for doing what is right. "Works" is a present tense, middle voice form, suggesting that one throws himself energetically into a steadfast mode of obedience. How can anyone read this and deny that "working" is an integral part of God's plan of salvation?
Obedience is imperative, as other New Testament passages teach. Jesus is "the author of eternal salvation to all [whether Jew or Gentile] who obey Him" (Heb. 5:9). "For in Christ Jesus neither circumcision [Jews] nor uncircumcision [Gentiles] avails anything but faith working through love." Peter, by inspiration, opened the door spiritually for Cornelius, his household, and all other Gentiles who were willing to fear and obey Almighty God. Surely Peter, at this point, fully understood the vision God had revealed to him earlier.