The Borg Queen exhibits hierarchical command structure, instead using a structure similar in principle to the internet with no control center and distributed processing. Star Trek: First Contact introduced the Borg Queen as the Borg Matriarch. The Queen is the focal point within the Borg collective consciousness and a unique drone within the collective, who originates from Species 125, that brings "order to chaos", referring to herself as "we" and "I" interchangeably.
Star Trek First Contact
The Borg Queen is seen as apparently present during Picard's former assimilation at the start as flashbacks in Picard's mind (a character formerly assimilated by the collective who's link was not completely severed), and was believed destroyed along with that Borg cube years earlier. Here, she instead directs her attentions to Data. After his capture by her drones, she tries to tempt him with live flesh to comply with her. This Queen is destroyed when her organic components are melted off as a result of Data's deception. She is destroyed in the Voyager episodes "Dark Frontier" and "Endgame", as well.
In the Star: The Experience attraction The Borg Invasion 4-D, the Borg Queen re-appears after Voyager returns to the Alpha Quadrant, but as Admiral Janeway attempts to kill her, she activates a transporter, allowing her to survive.
In the Star Trek: Voyager relaunch novels, the Borg Queen isn't a single, irreplaceable entity, but the product of a program called "The Royal Protocol" that shares its name with a Starfleet document outlining requirements when dealing with foreign royalty. This program is used to create a Borg Queen from any female Borg, commanding the technology within her to alter and adapt to the Protocol's specifications.
In the relaunch novels, one of the leaders of Starfleet Intelligence gets her hands on "The Royal Protocol" and, with the use of an Emergency Medical Hologram, turns herself into a new kind of Borg Queen who cares about and loves her drones.
In the video game, bonus content unlock-able through the course of the game further explains the role of the queen. It is suggested that the females of a particular species have a natural ability to filter and control the immense 'traffic' of thought present in the collective consciousness of the Borg. These females, in a sense, serve as regulators or signal boosters even, assisting in maintaining the complete consciousness over the thousands of light years of Borg space.
This also presents the possibility of multiple queens, which would be a suitable explanation for why two separate Starfleet captains have 'killed the queen'. In the illustration accompanying the explanation, all the females distinctly resemble the queen portrayed on screen.