This passage is a great example of Acts 1:8 being fulfilled. In chapter three, Peter and John healed a beggar who had been crippled for years. In chapter four, the Holy Spirit uses this healing in a powerful way to reach out to the entire city of Jerusalem. The religious leaders of the city were "greatly disturbed" because of this miracle and the preaching that followed. So, they arrested Peter and John hoping to intimidate them into silence and hinder this movement. They failed on both counts. The number of believers increased to more than 5,000, having started just weeks before with the 120 people who had witnessed the ascension of Christ. 
Acts 1:8 promises that God will give power to believers (now as well as then) so that they can speak about Christ in a supernatural way. Not only will believers have extraordinary courage but their words will also have great effect. When we yield our lives to Christ and trust His Spirit to fill us, He empowers us to do great things for Him.