Borg space or Borg territory referred to the vast Delta Quadrant space and territory controlled by the Borg. It included thousands of solar systems, all Borg, and millions of Borg vessels. (VOY: "Scorpion")
In 2373, it became clear to the crew of USS Voyager that they were entering the heart of the Borg's territory. There was no way around it, but the ship was able to pass through by leveraging their insight into Species 8472 to forge an alliance with the Borg, lasting just long enough to ensure safe passage. (VOY: "Scorpion", "Scorpion, Part II") Shortly thereafter, a leap of 9,500 light years made possible by Kes truly brought Voyager safely beyond Borg space. (VOY: "The Gift")
During the Borg-Species 8472 War, a narrow corridor within Borg space, nicknamed the Northwest Passage, was effectively cleared of Borg activity due to Species 8472 activity. (VOY: "Scorpion")
By late 2374, Species 116's homeworld had been assimilated and was located within Borg space. (VOY: "Hope and Fear")