I rather like it that I don't understand this character/plot element, either. Fancy finding something alien in a scifi show...
On the surface, it just looks as if the Borg hive mind sort of elected a leader of some kind. Perhaps she's more of a spokeswoman than an actual decider, though, even though her voice gives the final rubber-stamp to Collective decisions. In that, she could be like an insect queen, the lowest of slaves, reduced to serving the hive in some narrow and degrading fashion (whether it be laying of eggs, or communicating with enemies, or thinking on her own brain without being connected to the Collective).
However, there are more intriguing possibilities there. The Queen could be a feature of the Collective that emerged by accident, a parasitic lifeform the Collective would rather do without, but can't get rid of. Or the Queen could have come from outside and carved herself a cozy home in the Collective. Perhaps she is something that the Collective once assimilated but to their dismay got more than they bargained for, something the hive mind couldn't control?
It could be that the Queen has her own agenda, which only incidentally agrees with that of the Borg - the same way a parasite would incidentally wish for the survival of the host lifeform. Or the Queen could be slave to the Collective and work for the Collective agenda, but would most often be employed in sprouting disinformation: lying about her own status, lying about Borg plans, lying about how the Borg really viewed whomever was having this discussion with the Queen.
Certainly it could be argued that in ST:FC, the role of the Queen was specifically and even solely to confuse Picard and Data. A sort of PR specialist, or entrapping prostitute, or something of that ilk.