Harry Potter and the Prisoner of Azkaban, there's a definite interplay between setting the stage for future and coming to terms with past. You have to deal with the past and get it out of the way before moving on. And we have two types of pasts that people deal with here: personal memories (such as Harry's haunted, Dementor-triggered flashbacks) and collective, community memories (such as everyone's "recollection" of what crazy Sirius Black did to get a one-way ticket to Azkaban). Perhaps this is the reason for the absence of Voldemort in Book 3. If the Chamber of Secrets was about Voldemort as young Tom Riddle, then Azkaban is more about the characters' personal and collective memories of Voldemort during the height of his power.
The past also conveniently acts as an umbrella theme in the novel, meaning that it sort of encompasses all the other themes. More specifically, it's tied to themes of fear (see the lingering fears of all things Voldemort-related), themes of secrets (the past is a mystery that reveals itself to Harry), and themes of growing up (since part of growing older involves learning about and dealing with the past). The past is everywhere you turn in Book 3, so learning about the past and dealing with memories becomes a right of passage here that ultimately connects Harry to the wider wizarding world.