Now while Peter was inwardly perplexed as to what the vision that he had seen might mean, behold, the men who were sent by Cornelius, having made inquiry for Simon's house, stood at the gate and called out to ask whether Simon who was called Peter was lodging there. And while Peter was pondering the vision, the Spirit said to him, “Behold, three men are looking for you. Rise and go down and accompany them without hesitation, for I have sent them.” And Peter went down to the men and said, “I am the one you are looking for. What is the reason for your coming?” And they said, “Cornelius, a centurion, an upright and God-fearing man, who is well spoken of by the whole Jewish nation, was directed by a holy angel to send for you to come to his house and to hear what you have to say.” So he invited them in to be his guests. The next day he rose and went away with them, and some of the brothers from Joppa accompanied him. And on the following day they entered Caesarea. Cornelius was expecting them and had called together his relatives and close friends. When Peter entered, Cornelius met him and fell down at his feet and worshiped him. But Peter lifted him up, saying, “Stand up; I too am a man.” And as he talked with him, he went in and found many persons gathered. And he said to them, “You yourselves know how unlawful it is for a Jew to associate with or to visit anyone of another nation, but God has shown me that I should not call any person common or unclean. So when I was sent for, I came without objection. I ask then why you sent for me.” And Cornelius said, “Four days ago, about this hour, I was praying in my house at the ninth hour, and behold, a man stood before me in bright clothing and said, ‘Cornelius, your prayer has been heard and your alms have been remembered before God. Send therefore to Joppa and ask for Simon who is called Peter. He is lodging in the house of Simon, a tanner, by the sea.’ So I sent for you at once, and you have been kind enough to come. Now therefore we are all here in the presence of God to hear all that you have been commanded by the Lord.”
some of the brothers - There were six of them (Acts 11:12).
"The case of Cornelius was the first of its kind and crucial to the spread of Christianity. It answered the question, 'Can the new faith (still so closely associated with Judaism) admit into fellowship an uncircumcised Gentile?' The issue, however, would not be completely resolved for some time." (Ryrie) [Notice that Ryrie sees things differently than Stam below.]
"Peter could not take such a command lightly. It was the law of God by Moses, and to disregard it was a serious matter. When the Lord was with the apostles on earth, He Himself had scrupulously obeyed the law and had taught His disciples to obey it. He had even called upon His followers to 'observe and do' all that the scribes and Pharisees commanded, simply because they occupied Moses' seat of authority (Matt 23:1-3). And this was carried over even into the 'great commission' for there, after His resurrection, the Lord commanded the apostles to make disciples of all nations, 'Teaching them to observe all things whatsoever I have commanded you ...' (Matt 28:20). From the record of Acts it is further clear that the followers of Christ, contrary to prevailing notions, had been careful not to start a sect separate from Judaism and had faithfully observed the law. These were the true Israelites, who accepted Christ as their Messiah, and there had as yet been no revelation to the effect that the Law had been done away, nor do we find any such revelation until it is given through Paul." (Stam)
"The Israelites were, indeed, denied the 'unclean' meats of which Gentiles freely partook (Lev 20:25). They were also forbidden to make covenants with the Gentiles or to intermarry with them (Deut 7:2-3; Ezra 9:2) and thus a distinct separation was maintained between them, but we know of no explicit injunction prohibiting any association at all with those of other nations, nor even of doing business with them. Indeed, as we have already seen, the Israelites were specifically instructed to deal kindly with Gentiles who had come among them and treat them as those born in their midst (Lev 19:33-34). Certainly Cornelius, a God-fearing man, and living, as he did, in Palestine, was entitled to this sort of treatment as far as Moses' law was concerned. In what sense, then, had it been 'unlawful' for Peter to even visit Gentiles, and why did his fellow apostles call him to account for so doing? ... We believe the key to this problem is to be found in our Lord's first commission to His twelve apostles (Matt 10:1-7). Here the apostles were specifically instructed: 'Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not' (Matt 10:5). While our Lord had as yet sent forth only these twelve, this rule would, of course, apply to any Jew, even though those who were indifferent or antagonistic to His claims would not recognize it. As we know, our Lord Himself also kept aloof from the Gentiles during His earthly ministry. He did help one Gentile man and one Gentile woman, but they came to Him for help, and at least in the latter case He made it very clear that He had not been sent 'but unto the lost sheep of the house of Israel' (Matt 15:24). We know that our Lord did not follow this course because of lack of love or pity for the Gentiles, but because He recognized the divine play of covenant and prophecy to send salvation to the Gentiles through redeemed Israel (Gen 22:17-18; Zech 8:13, 23; etc.). So far as the revealed program of God was concerned, Israel must first be saved before salvation could be sent to the Gentiles. Thus our Lord said to the Gentile woman referred to above: 'Let the children first be filled' (Mark 7:27). Our Lord did not change all this after His resurrection, for under the so-called 'great commission' the apostles were explicitly instructed to begin their ministry with Israel (Luke 24:47; Acts 1:8). This was with the assumption, of course, that Israel would now receive Christ, and that salvation could then also be sent to the Gentiles. Surely Peter makes it clear in Acts 3:25-26, that Israel must first be saved, so that salvation might flow through her to the Gentiles. In view of this, it is natural that Peter had considered it 'unlawful' to go to the Gentiles, for Israel had certainly not yet been saved. Indeed Israel had declared war on Christ (Acts 8:1-3). But now the prophetic program was to be interrupted by the dispensation of the grace of God. God, in infinite grace, had already reached down to save Saul, the leader of the rebellion, with a view to sending him to the Gentiles, Israel's obstinacy notwithstanding. To pave the way for this and to ensure the recognition of Paul's subsequent ministry by the twelve, God had now sent Peter to the Gentiles, even though Israel remained unrepentant. Peter, then, had been in perfect harmony with the will of His Master, and was in perfect harmony with it still as he now went to the Gentiles. Note carefully the exact wording of his statement in Acts 10:28: '...it is an unlawful thing for a man that is a Jew to keep company, or come unto one of another nation; but God hath showed me that I should not call any man common or unclean.'" (Stam)
"Let us not confuse this, however, with the revelation of the mystery to Paul. Peter was not told that there would be any change in the program. He was not instructed to continue going to Gentiles. He was imply instructed to go to this one household and, so far as Scripture is concerned, we have no record of his ever ministering to Gentiles again. In fact we find him shaking hands with Paul, solemnly agreeing to confine his own ministry to the circumcision, while Paul goes to the Gentiles. It is evident from the record, that Peter did not understand what God was doing. He was simply commanded to go 'doubting nothing' (Acts 10:20) and when he ministered to Cornelius and his household, God took the matter out of his hands, so that 'they of the circumcision were astonished' as the Gentiles received the Holy Spirit (Acts 10:44-45). In defending his action before the other apostles Peter could say only: 'What was I that I could withstand God?' (Acts 11:17). Peter, then, did not receive the revelation of the new dispensation to be ushered in, any more than he used 'the keys of the kingdom' on this occasion, but he did receive a vision and instructions to go to this one Gentile household, and it was on the basis of this incident that the Church at Jerusalem later recognized Paul's ministry among the Gentiles. How could they object, since their own Christ-appointed leader had himself been sent to the company of Gentiles apart from the conversion of Israel?" (Stam)