Jesus is quoted in Acts 1:8 saying "But you will receive power when the Holy Spirit comes on you; and you will be my witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth." The reason for the Holy Spirit coming upon these disciples was so that they could have power to be a witness to Jesus.
A witness is someone who has seen something and has firsthand information. This to me is intriguing. If, as it is commonly done, we apply these verses to all Christians making us all witnesses - which I too think is correct, what are we firsthand witnesses of? Certainly not Jesus as He was in Israel. We, like Paul, are witnesses of the exalted Jesus.
But why would we need power for this? Why would we need the power of the Holy spirit coming upon us for this? I don't think that what Jesus was simply referring to was some synchronization with what we say and the conviction of the Holy Spirit in the heart of the listener, although true as far as it goes. But the power is given so that our claim that Jesus is Lord of all could be demonstrated with action, not in words alone.
This is why Paul wrote in 1 Cor 2:4-5 NIV "My message and my preaching were not with wise and persuasive words, but with a demonstration of the Spirit's power, so that your faith might not rest on men's wisdom, but on God's power." It is an essential part of our witness to demonstrate the veracity of our claim that Jesus is Lord. This is demonstrated by the Holy Spirit, who is supposed to be on us, seen by the acts and signs of power. Without this supernatural demonstration our witness is just another ingredient in the plurality soup.
The Jesus we have come to know is indeed Lord of all. This is our eyewitness claim. We declare that he is exalted to the Father and to prove it He has poured out the Holy Spirit upon us. (please note the italicized words - on not in) These supernatural gifts of the Spirit and the resulting love of the Spirit reproduced in our lives is our gift to the world to demonstrate the living reality of Jesus. We are witnesses.