At the end of Acts 9, Peter entered the room of a dead woman and said, “Tabitha, stand up.” NJB He was among believers, so did not need to use the in the name of Jesus, phrase. The power of God brought many in Jaffa to believe.
But Peter ended up staying in the home of a tanner. Within the social hierarchy of Israel, none were lower than tanners. They handled the hides of dead animals. Even if the animal had been a sheep sacrificed at Passover, it was dead and the tanner worked with it; he was as unclean as a person can ever be. We are not told why Peter ended up there, but it fits with the story of chapter 10.
A God-fearing Roman Centurion named Cornelius was instructed by God through an angel to invite Peter for a visit. He sent three men to find him, having been told he was in Jaffa. As they traveled, Peter entered into prayer with God but fell asleep. He still had that problem.
God visited Peter in a dream by showing him all kinds of animals, including snakes and pigs. God told Peter to eat of all of them. Peter said he could not and God repeated the image two more times before Peter awoke and realized the meaning of the dream.
Then God instructed Peter to go to the door and go with the men who were asking for him. At the home of Cornelius, Peter shared the Gospel.
Now for the important point: Cornelius and his whole Gentile household were filled with the Holy Spirit. The Messianic Jews who were there, many having traveled with Peter, were amazed that the Holy Spirit of the Most High God would fall on Gentiles.
It should not have been a surprise. The Old Testament is filled with the idea that God loves everyone and expects to save everyone. As David put it:
Sing Yahweh a new song
For he has performed marvels,
His own right hand, his holy arm,
Gives him the power to save. NJB
Be righteous and do good.