Peter and John immediately reveal the power and authority which the Holy Spirit within them has empowered them with by healing a man born lame. In echoes of the way Jesus demonstrated His Messiahship through acts of healing, so the Holy Spirit gives evidence of His presence by transforming peoples' lives. The miracle was accomplished just as Jesus' were: immediate, complete, life transforming.
There are some other things here: the apostles continued to exercise the habit of regular attendance at the Temple. The new faith and the old discipline could go hand in hand. These very early days of the Church were not marked by persecution from either the Roman authorities or the Jewish religious leaders, but we will very quickly read of the disintegration of this relaxed attitude to these believers in Jesus.
Peter uses the opportunity to preach once more to those who have gathered around this man once unable to walk. His themes include:
1. The crucifixion was the most shameful act in human history. Peter and the apostles were still reeling from what they had experienced. Remember this is probably only two or three months since the death of Jesus, but in all their recorded preaching, they never tried to lessen the visceral suffering of Jesus in His death.
2. Along with this, the early preachers stressed the vindication of the resurrection. Without this event, the Church would never have come into being. The resurrection was proof that Jesus was indestructible and the Lord of life and of death.
3. The early preachers never took the credit for themselves: they were very fast to give the glory to God. At one event in the book of Acts, some of the apostles-Paul and Barnabas- are worshipped by the crowd as gods- Acts 14 v 11-18- and immediately declare themselves human in the same way as each one there. They are horrified by the notion! They were very aware of their own limitations, but in parallel, knew that there was no limitation to what the risen Christ would do THROUGH them!