Which part of Acts 3? This?
Act 3:19 Repent ye therefore, and be converted, that your sins may be blotted out, when the times of refreshing shall come from the presence of the Lord;
19 Repent ye therefore, and be converted, that your sins may be blotted out, when the times of refreshing shall come from the presence of the Lord.
20
And he shall send Jesus Christ, which before was preached unto you:
Vs 20 is the critical part of Peter's sermon to Israel in Acts. Remember the final question the 11 asked Jesus before he ascended? Acts 1
6 When they therefore were come together, they asked of him, saying,
Lord, wilt thou at this time restore again the kingdom to Israel?
Peter's preaching to Israel in early Acts had a simple objective, "Convince the nation to repent of their crucifying of their Messiah and be baptized into their priesthood (Exodus 19:4-6), and then Jesus will come back to rule from Jerusalem, and usher them into the kingdom".
When Peter healed the man who was lame from birth, at the beginning of Acts 3, it was a sign to Israel that even though they were born lame since Abraham, Issac and Jacob when they kept rejecting the Father, the moment they believe in Jesus, they will leap for joy and finally enter into that promised Kingdom.