Peter recognizes that in Jesus Christ the Jews will find the fulfillment of this prophecy from Hosea. There were Jews who would have heard Peter's words and been infuriated. The Jews who loved Jesus Christ would have embraced Peter's words. They would have delighted to see that God was fulfilling his prophetic word and calling the Jews to himself again and calling them his people, his children.
The great challenge for all who would read Peter's words was to recognize that Jew and Gentile were now both considered to be the people of God. Salvation was for all people, not just the Jews. All this is possible because of the mercy of God. It is not because of the goodness of the Gentiles and their works. Salvation was not possible because of the Jews' efforts to keep the Law. Salvation is about the great mercy of God!
At one point in your life you were not considered one of God's people. Do you remember when you first received God's mercy? Give him praise. Share with someone how they also can be a part of the children of God. It's about mercy!