The overall purpose of Acts is not to explain the Holy Spirt — i.e., as if Acts were a treatise on a single person of the Trinity. Yes, we could say the Spirit is the central character, and we can gather some theology of the Spirit from these narratives, but there is a much broader intent. After all, Acts is a narrative, not a systematic textbook. Thus, the central purpose can be worded in various ways, but most expressions will sound something like “to demonstrate the spread of salvation among all nations” or “to describe the fulfillment of God’s promise for the world” — with key parts being (1) promise-fulfillment, (2) salvation, and (3) humanity.
The outline of Acts reveals this quite clearly. By looking at the various parts — or the structure of how Acts is organized — readers can observe a geographical movement from Jerusalem out to the broader world. Thus, Acts 1:8 serves as a central verse that provides for the entire book, and Joel 2 and Acts 2 remind us that Acts is not about charismatic gifts, but a visible demonstration of God’s outpouring to all people. To clarify, the geographic movement is used to emphasize that God’s grace has now been extended to all kinds of people, even those who the Jews perviously thought were unclean.
That being said, we also should avoid the opposite extreme of diminishing the Spirit. Chapter after chapter, Luke describes the growth of the Church, but Acts is far more than a handbook for church growth. We can gather understanding of mission from Acts, of course, but the book should not be reduced to a how-to manual, or something that we as humans can accomplish on our own. As the “sequel” to Luke’s gospel, the book tells of God’s miraculous work, which began in Christ and continues through the Holy Spirit. Only God could accomplish such extraordinary things, and we as readers are invited to participate in God’s incredible plan of salvation — which is not merely for a few in an upper room, but for millions around the globe.