Borg Queen

The Borg Queen is the apparent leader of the Borg Collective throughout the history of the Borg there have been a number of Queen's who seem to take on the same character perhaps indicating the Queen is persona within the collective which could in theory occupy any drone.

Creation
There are a number of theories as to how the Borg Queen came to being:

The Beginning
The Borg Queen was subject of a world which had been struck down by a deadly disease which was slowly killing much of the population. The scientists on the planet developed bio-organic regenerators, a nanotechnology which would be injected into a subject's circulatory system, eradicate the disease and rebuild the patients crippled body. The Queen to be, in very ill health, was selected to be the subject of the first experiment. It was successful in eliminating the disease but also began to change her, making her stronger than ever before, replacing her broken body with technology and giving her drive and determination to share her gift with others and make them as perfect as her superior self had become. The establishment attempted to resist but the Queen was not willing to let herself be destroyed and instinctively used the nanoprobes to assimilate others. She quickly lead her drones in assimilating the entire planet and set to work to spread her gift to the rest of the galaxy. (SNW VI short story: "The Beginning")

Side Effects
Alternatively: The Borg Queen was originally a woman named Danzek who was the daughter of a scientist named Mynzek. Mynzek, with the aim of finding a cure for a terrible disease established a research base near the event horizon of a black hole. He sent ships out via a series of wormholes to capture subjects and run experiments on them in the search for a cure. Using the gravitational time dilation effect of the black hole he could coordinate centuries of research being conducted on the ships which for those on the base took only days. Danzek was the guinea pig for these experiments on one ship, integrated with technology and biological components from numerous races she became powerful and returned to the station controlling a group of drone like test subjects. After a brief confrontation the station was destroyed, Danzek, queen of her subjects escaped through a wormhole, which thanks to the temporal distortion generated by the exploding station could have sent here anywhere in space and time. (TOS manga: Side Effects)
 * ''The short story “Forgotten Light” offers another version of the Borg's creation but not one in which the queen was the catalyst for change, it is possible that Sivdar, the leader of the technologist,s a group who pushed for the technology which created the Borg in this story could have taken on the role of Borg Queen.

Purpose
The Queen appears to lead the Borg, having total control over the entire collective, however it is possible she acts as a figure head, a voice for the Collective much like Locutus. When it appears she is ordering the collective she may simply be enacting the collective's will. As the Queen is also part of the collective it may be possible she stands in the mid ground, part of collective decision but filtering out the best ideas herself, bringing "order to chaos". (TNG movie: ''First Contact, et al.)
 * "The Beginning" and "Side Effects" would seem to indict the Queen is purely a leader, however "Forgotten Light" shows the Collective developing with equality.

History
By 2375 the Borg Queen was a member of Species 125. (VOY episode: Dark Frontier)
 * Assuming the Borg designated their progenitor race Species 0 or 1 this would seem to indicate by this time the Queen had been replaced at least once.