"And the apostles and brethren that were in Judaea heard that the Gentiles had also received the word of God." - Acts 11:1

When Peter came up to Jerusalem, the Jewish believers (“they that were of the circumcision”) criticized him for going into the home of Gentiles (uncircumcised men) and eating with them. (Acts 11:2-3)

Peter began telling them the story of Cornelius. (Acts 10:1-48).

"And he shewed us how he had seen an angel in his house, which stood and said unto him, Send men to Joppa, and call for Simon, whose surname is Peter; who shall tell thee words, whereby thou and all thy house shall be saved." - Acts 11:13-14

What words did Peter speak to the Gentiles?

He spoke of the message of peace through Jesus and all Jesus did throughout the land of the Jews and in Jerusalem, whom they slew and hanged on a tree, but He rose on the third day and was seen openly. (Acts 10:36-40). Peter told the Gentiles how Jesus commanded them to preach unto the people, and to testify that it is Jesus who will be the Judge of quick and dead. (Acts 10: 41)

Then Peter told them, "To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins."  (Acts 10:43)

"And as I began to speak, the Holy Ghost fell on them, as on us at the beginning." - Acts 11:15

How did the Holy Ghost fall on the Jewish believers in the beginning, on the Day of Pentecost?

 "And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance." - Acts 2:4

"Forasmuch then as God gave them the like gift as he did unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God?" - Acts 11:17

"When they heard these things, they held their peace, and glorified God, saying, Then hath God also to the Gentiles granted repentance unto life." - Acts 11:18

[At the house of Cornelius: "Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days." - Acts 10:47-48]