As you might deduce from the title, this may be the nerdiest post I've ever made.
The obvious interpretation for the Borg Queen is that it's a creation of the Borg designed to coordinate and direct Borg activity. It also acts as an ambassador/negotiator with other races. In terms of drama, the Borg Queen serves as the "face" of the Borg; it's not very interesting to have a conflict with hundreds of identical faceless opponents.
Any nerd can tell you that the Borg don't need a Queen. Even if they needed the mental capabilities of the brain, the Queen could simply be a thinking drone. Billions of minds that can somehow instantly reach consensus are infinitely more valuable than any individual. And the Borg do just fine without any individual negotiator, they can converse as a hive with no difficulty.
So why the Queen? My (Non-Canonical) explanation is simple, the Borg Queen is not an intentional creation of the Borg designed to aid in operations, she is a Parasite. The Borg are like a colony of insects, and like ants and bees, they're more vulnerable from the inside than the outside. If a Borg gained the ability to send out a directive in such a way as to simulate the "hive mind" of the Borg as a whole, it would be like an insect that was being fed by an ant colony, because it was emitting appropriate pheromones. Its whim would be interpreted by Borg as the Collective's decisions. Almost immediately, we have a Queen. The Borg wouldn't be able to interpret the Queen as a threat, or an imposition. Their thoughts and actions would be dictated by the Queen in a way far more profound than any biological equivalent in our ecosystem.