The Collective's primary goal was to bring order to chaos, to achieve biological and technological perfection by assimilating unique and more advanced attributes from other races, and at the same time help share the Borg's increasing perfection by adding said assimilated species to the Collective. (TNG novelization: Star Trek: First Contact)
The Borg's desire to obtain perfection led them to go to great efforts when they encountered something they considered especially worthy of assimilation. For example, they invaded fluidic space in order to assimilate Species 8472, which they considered the pinnacle of biological perfection. Or chasing sensor ghosts on Lythos Prime when they believed they had found a hybrid carbon/silicon-based lifeform (in fact jumbled readings of Humans and Horta). (VOY episode: "Scorpion"; ST comic: "A Rolling Stone Gathers No Nanoprobes")
The Borg Collective consisted of the minds of each individual Borg drone, technologically linked to one-another through a subspace frequency, altering the thought patterns of each drone and yoking it to the Collective's guiding will. The Collective was generally directed by the Borg Queen, who operated in much the same way as a queen bee, with the drones functioning as worker bees. Borg Queens were created through the implementation of the Royal Protocol in a female drone, creating a replica of the guiding intelligence. However, both the minds of the individual drones and the mind of the Borg Queen were themselves controlled by a deeper will: The degenerated mind of the Caeliar once known as Sedin, reduced to a state of pure hunger and malice. (VOY novel: The Farther Shore; ST - Destiny novel: Lost Souls)
The Collective was structured around the hive mind which interconnected each drone via the neural interlink frequency generated by the Vinculum at the heart of every Borg vessel. (VOY episode: "Infinite Regress")
The Collective was divided into organizational sub-sections, the largest being the unimatrix and further subdivisions being the trimatrix and adjunct. (VOY episodes: "Dark Frontier", "Unimatrix Zero", "Endgame")
- See main article Borg history.
The Borg Collective first came into existence in 4527 BC. That year, the temporally displaced Caeliar known as Sedin forcibly bonded with three Humans from the 22nd century: United Earth Starfleet Lieutenants Karl Graylock and Kiona Thayer and United Earth MACO First Sergeant Gage Pembleton in a bid to survive the destruction of the Caeliar city-ship Mantilis in the frozen antarctic wastelands of Arehaz in the Delta Quadrant. Reduced to a state of pure hunger after having murdered her Caeliar compatriots, Sedin used her catoms to possess the minds and bodies of the three surviving humans, transforming them into the first drones. She had Graylock and Thayer kill Pembleton and eat his body to survive, then ordered them to sleep. Upon the arrival of a Kindir icebreaker later that year, Sedin and her newly formed Collective targeted Arehaz for assimilation. In consequence of the final free thought of Lieutenant Graylock imprinting upon the Collective consciousness (that he would not become a cy-borg), the new collective entity referred to itself as the Borg.
Due to the damage to Sedin's mind, she lost most of her memories of her past. However, at least some residual memory of her people's power source - the Omega molecule - remained. This led to the Borg's obsession (almost reverence) with the Omega Molecule, believing that assimilation of this molecule would give them perfection. Fueled by human aggression and Caeliar paranoia and rigidity, the Collective developed a ruthless agenda to assimilate or destroy everything in its quest for perfection. (Star Trek: Destiny novel: Lost Souls.)
Apart from some limited exploration the Borg presence remained mostly in Delta Quadrant until the mid-24th century when they encountered a Federation starship and began to target Humanity. After that first contact, the Collective quickly established itself as a major threat to the races of the Alpha and Beta Quadrants in the numerous incursions and assimilation attempts that followed.
After thousands of years of conquest and assimilation, the Collective was finally dissolved in 2381 when the Caeliar gestalt discovered and removed Sedin's corrupted essence from the Collective. As a result, trillions of drones were freed and subsequently absorbed into the gestalt.
In an alternate reality, the Borg Collective had succeeded in conquering the Federation and much of the Alpha Quadrant by 2370. The USS Enterprise-D was one of the last surviving Federation starships by this time. (TNG episode: "Parallels")
In another alternate reality in which the Borg Collective had prevailed at the Battle of Wolf 359 in 2367, the Borg occupation of the Alpha Quadrant had spread to the Bajor sector by 2371 and Deep Space 9 had been assimilated. While the USS Defiant of another reality was travelling between universes in 2371, it discovered the assimilated DS9 and was fired upon by a Borg cube before escaping to a different reality. (DS9 comic: "The Looking Glass War")