The title is pretty much a straight-forward description of what the book is about. There's no mystery there, no suspense, no puzzle to figure out like in some other books we know.
Alexander and the Terrible, Horrible, No Good, Very Bad Day is what you might call the opposite of that—and with great purpose. Viorst gives us four ways to say "rotten" in order to emphasize just how bad this day seems from Alexander's point of view.
But the title introduces the humor in the book's narrative voice, too. Remember when you were a kid and the biggest number you could think of was something like a hundred billion sixty three hundred seven thousand hundred? Saying things a lot of times was pretty much the only way you knew how to emphasize how much you really meant it.
The same is true for describing this day…or the feelings involved in it. All of the synonyms in the title exaggerate the quality of Alexander's day, and at the same time reveal just how, well, immature he is.
He's a kid, remember?