Before we ask this question, let's take a couple steps back and consider what a title is for. Titles don't exist so we can catalogue our film collections in alphabetical order. You can go chronological order, or for the truly obsessed, there's always autobiographical. Titles exist long before the movies reach our cabinet shelves and digital streams, and they are crafted to serve two primary purposes.
Purpose numero uno: a title should intrigue viewers to watch the movie. There's a reason nobody has watched The Englishman Who Went Up a Hill but Came Down a Mountain, and it ain't the acting. On the other hand, who doesn't want to watch something called Mad Max: Fury Road? You read that title and you just know that movie with be a feast of awesome for your eyes. (And it is!)
As for numero dos, a title should point viewers to an important quality of the story. It can be a character, like Amélie; a group, like Goodfellas; a place, like Casablanca; or a concept, like Apocalypse Now. All of these titles provide viewers the first clue to unlocking the puzzle box that is movie's story, characters, themes, symbols, and so on.
Monkey See, Monkey Do
12 Monkeys manages the first task with aplomb. You read that title and immediately ask, "Huh, what type of situation involves a dozen monkeys and Bruce Willis?" You just have to sacrifice an afternoon to answer that question.
But when it comes to the second purpose, things get a little more complicated. In Amélie, there is a character named Amélie, and we follow her story from beginning to end. Casablanca takes place in Casablanca. But there are hardly any monkeys in 12 Monkeys, and certainly not a dozen.
The only plausible option is that the title refers the Army of the 12 Monkeys, but the organization turns out to not be all that important. Sure, we hear about the organization over and over from Cole and the future Scientists, but its members appear only at the end. They don't even release the virus, and instead turn out to be a bunch of ineffectual environmentalists pulling a prank.
Ah, but we've stumbled onto the point. The title 12 Monkeys is pulling a prank on us, the viewers.
Even if subconsciously, we assume the Army of the 12 Monkeys will be important because of the title. When we first hear about the Army of the 12 Monkeys, our ears perk up. 12 monkeys? That's in the title. Must be important. As we hear more and more about the organization, we interpret it them to be more important.
This is important because the film is all about toying with perception. Consider this telling scene:
COLE: I was right. They're here! You see? Twelve Monkeys. Twelve Monkeys. Do you believe me now? Come on! Come on! They're here. You see? Twelve Monkeys! Twelve Monkeys. Come on! Wait…here, here! Do you see? You see?
RAILLY: I see some red paint, some marks.
COLE: Marks? Marks?
Cole and the Scientists perceive the Army of the 12 Monkeys to be important, so they put their resources and energy into following a dead end. Dr. Railly perceives Cole to be insane, so she can't see the world like he does. All she sees is red paint. Likewise, we think the Army of the 12 Monkeys must be important until late in the film when events alter our perception.
The title pre-shades our perception before we even watch the film, and this fact makes us participants in the theme of perception. Like the film's characters, we've had worldviews instilled into us, and it takes a lot for us to realize that those views may be wrong.
Rather than simply teaching us this lesson in the story, the movie, through its title, allows us to experience it firsthand. Come to think of it: it's as though we were monkeys in the movie's lab.