Acts of the Apostles is kind of a tough one to nail down, genre-wise. In a way, it's similar to ancient histories or biographies. It's obviously trying to record the background of the early church and tell the tale of the individual people that worked to spread the gospel after Jesus died.
But it's also more than that. It has tons of sermons and also works like an apology. No, that doesn't mean that Acts is sorry to have bumped into you on the subway. An apology is a work that provides a defense or justification for something. This one is a defense of Christian faith that helps provide readers with arguments to convince others to follow Jesus. Finally, it's also a little bit like a novel because it's just so darn entertaining. Only in the Bible will you get four genres rolled into one (source).