What does Acts 4:1 mean?

One day, while going to the temple to pray, Peter and John came upon a lame man asking for alms. Instead of money, Peter gave him the ability to walk. The people on the Temple Mount, many of whom recognized the man now leaping about, swarmed Peter and John. Peter used the opportunity to tell them Jesus of Nazareth gave them the power to heal—the same Jesus the leadership and people of Jerusalem had killed. But this same Jesus rose from the grave and now provides a way of reconciliation with God (Acts 3).

Priests are descendants of Moses' brother Aaron and are responsible for the ceremonies within the temple. By this time, they make up a powerful political bloc. The temple guards are relatives of the chief priests and are responsible for keeping order on the Temple Mount. They are not the Roman soldiers stationed at Antonia Fortress on the northwest corner of the Mount. Sadducees are members of a Jewish sect. Unlike the Pharisees, Sadducees do not add extra rules to the Mosaic law, they like the Romans because of the business opportunities, and they don't believe in the resurrection. Most of the chief priests—and most of the Sanhedrin, the Jewish ruling council—consider themselves Sadducees.

Jesus didn't interact with the Sadducees as much as the Pharisees because the Sadducees tended to stay around Jerusalem. The week before the crucifixion, He did debate with them at the temple, proving from God's own words that the resurrection from the dead is true (Mark 12:18–27). Peter's teaching that Jesus rose from the grave catches their attention.