Let’s bring in the context. In the previous verses Jesus revealed that with the coming of the Holy Spirit, certain things would be put under the disciples’ power, and He proceeded to speak of them being His witnesses. The power to witness the Gospel to others has been delegated to us, the disciples of Jesus, and is not under God’s direct control.
Not even angels are allowed to preach the Gospel for us (Acts 10:3-5). We have received the power to be witnesses. It is not by God’s choosing that some have still not heard the Gospel. It is because we have not been faithful to be His witnesses.
The Greek word used for “power” here is “DUNAMIS,” and it means “miraculous power” (Strong’s Concordance). This word was also translated as “ability,” “might,” and “strength.” It is the root word from which we derive our words “dynamic” and “dynamite.” This clearly speaks of the presence and anointing of the Holy Spirit as being the power source in the believers’ lives.
It was this anointing power of the Holy Spirit that worked miracles in the life of Jesus (Acts 10:38).
The Lord has empowered us to be witnesses, not the judge and jury. Witnesses simply relate what they have experienced, thereby providing evidence to true of something. We are to witness in word and deed to the truth of Jesus being alive in us, and let God be the one who convicts (John 16:8).
Jesus specified an orderly progression in the way we should be His witnesses. First, we start in Jerusalem (i.e., where we live). Then, we go to Judea (nearby). Finally, we take the Gospel to Samaria (elsewhere.)