The context of Acts 10 deals with the Gentiles being revealed as gospel subjects. The prophecies had been clear concerning this fact – “After this I will return and will rebuild the tabernacle of David, which has fallen down; I will rebuild its ruins, and I will set it up; So that the rest of mankind may seek the Lord, even all the Gentiles who are called by My name, says the Lord who does all these things” (Acts 15:16-17 – James quoting Amos 9:11-12). Jews had no dealings with other peoples. Peter would need great convincing.
Peter fell into a trance and saw an “object like a great sheet bound at the four corners.” This sheet-like object held unclean animals. God had prohibited His chosen nation from eating certain meats to serve a purpose of His. Peter, being a Jew, observed this law. However, God’s purpose had been served, and “What God has cleansed you must not call common.” The Lord commanded Peter to eat. This occurred three times. God made sure Peter was impressed with this vision so as to provoke wonder within him (v. 17).
Peter, being met by Cornelius, later learned the meaning of the vision (v. 28). Gentiles are gospel subjects. Cornelius and his household were later saved after having heard the gospel presented by Peter. They were baptized in water for the remission of their sins (v. 47). It is wonderful that our God shows no partiality (v. 34)!