Harry Potter books tend to follow a certain formula, which is cool to consider. They start off with Harry's birthday. And they end with Harry returning to the Dursleys' house for yet another summer. The ending of this book is no exception to this format. After yet another adventure, Harry and his BFFs journey home on the Hogwarts Express, and Harry manages to sneak in another "gotcha!" moment when he reunites with the Dursleys. This year it's "Oh, did I forget to mention that my godfather is an escaped convict?" Good times, Harry.
However, this ending does stand out a bit from the previous two books in that Harry now has new family members in his life and a connection to his parents that he didn't have before. Sirius's letter to Harry at the end points to how things are going to be changing for Harry in the future – he's connected not only to his past but to the entire wizarding world more fully now (through his knowledge and through his ties to Remus Lupin and Sirius). The ending of this novel fittingly sets the stage for the more adult novels to come in the series.