Peter and company were surprised by how many people had gathered to hear. Cornelius had invited his relatives and close friends. This is beautiful. It is what god-fearing people do! He had God's word that he would discover life and he wanted it for his friends and family, too.
Peter's response to the explanation behind his invitation and his own vision was to say, "Now I now there is not favoritism with God!" The he points out that Jesus was not revealed to just anybody, but to those who had been selected beforehand! Those two go together, God's selection and no favoritism. The pouring out of the Holy Spirit sealed the deal and assured them of that truth.
The sermon here is a summary of the gospel being in the Old Testament, through the life, death and resurrection of Jesus. This is the content Cornelius must have to be saved!