Symbolism, Imagery, Allegory
We never actually see Azkaban in the book – none of our main characters go there (thank goodness). But it's in the title and the presence of Azkaban is felt throughout all of Book 3. Azkaban works overtime as a symbol in the book – it represents themes of death and fear through its Dementor guards; themes of entrapment and imprisonment, of course; and themes of isolation, since it's an inaccessible island prison much like a real-life prison with a similar name: Alcatraz. It also ties in to themes of mystery, since Harry and his friends know little about the place. Adults seem reluctant to discuss it and overall the prison maintains a fairly forbidding aura.
So it's significant that Harry and his friends never see Azkaban in person in this book; seeing it for themselves would undermine the themes of fear and mystery that Azkaban represents in the novel. And not seeing the prison, in a book that's largely about imprisonment, helps to emphasize how prisons come in different shapes and forms and aren't just Alcatraz-like jails on tiny islands out at sea.