I've always heard Acts described as being the story of the early church. While it describes events relating to the early church, it is hardly a story about the early church. What I mean is, the early church is not the main character of Acts.
So, who is the main character? Well, let's think through an outline of Acts...
We begin with Jesus, post-resurrection, pre-ascension. He talks with the Twelve, reminding them of the things He had told them before. He reminds them of the "Great Commission" and then He ascends.
(On a side note, when Jesus ascends, the disciples - and others - stand googlie-eyed, staring at the sky and a couple of angels - uh, men in white robes - come and say, "hey guys, what's up?" And they say "Uhh... Jesus? (this is said in a perplexed tone filled with bewilderment) He just ascended into the clouds..." (of course they do this without taking their eyes off the sky) and the angels say "in the same way He left, He'll come back." Most sermons will teach us that Jesus will descend from the clouds. Could be. But its more fully supported to argue that "in just the same way" means that He will come unexpectedly, just as He left unexpectedly... Food for thought.)
So Jesus is gone, and who takes the main spot next? The Twelve, with Peter at the forefront. Pentecost happens and Peter and the Twelve preach and many are saved. Peter remains in the spotlight for a while, but before you start to think Peter is the main character he more or less leaves the story. In chapter 6 the Twelve select the Seven, two of which are Stephen and Phillip and we find Stephen taking the spotlight and by chapter 7, he is preaching (a very eloquent speech if you ask me!) and becomes the first martyr. So, Peter is out and Stephen is out.
The story doesn't turn back to Peter, but instead briefly introduces Saul and then we find Phillip preaching. The narrative then returns to Paul and, with few - if any worth noting - exceptions, follows Paul from then on.
So some argue that Acts is about Paul - his conversion and his ministry. But that doesn't jive. He isn't even present, except for a brief mention of his presence in chapters 7-8, during the first 1/3 of the book. Hard to believe he is the main character.
So who is present throughout?
The Message. The Message which Jesus reminds the Twelve (which is actually down to Eleven at this point) of before His ascension. The Message which Peter preaches. The Message which the Twelve - err, Eleven - preach. The Message which Stephen and Phillip preach. The Message which Saul receives and Paul preaches.
So, what is the book of Acts about? The Message and its spread throughout Jerusalem, Samaria and the uttermost parts of the earth.
