Acts 4:5-12 is filled with irony.
Peter and John have been arrested because they have been "proclaiming in Jesus the resurrection from the dead." The next day, they are brought before an intimidating group of powerful and important people. These religious authorities ask Peter and John what authority they have to be teaching the people in this way. Peter, although he is uneducated and untrained (v.13), speaks boldly to those in power saying that it is in the name of Jesus that they teach the resurrection and that a crippled man was healed. Peter even goes so far as to say that it is "by the name of Jesus Christ the Nazarene, whom you crucified, whom God raised from the dead - by this name this man stands before you saved."
This is the fundamental irony of the passage that leads to all the rest. The one who was rejected, despised, and crucified by the religious authorities was raised from the dead by God himself. Those in power, the trained and educated theologians, the ones who were supposed to know the heart of God the best, put to death the only one by whom all people must be saved. In contrast to these ungodly ones who are supposed to be godly, God raises Jesus from the dead - and so the universe begins to be turned upside down. Once the process of death itself is overturned, it is hard to imagine what can't be. The crippled begin to walk. The powerless and uneducated speak boldly and prophetically to those in power. The crucified can be the savior of the world. We might even go so far as to believe that God could take us - broken and scarred sinners through we are - and begin to transform us into ambassadors of life breathing resurrection power in our world.