The Gamma Canaris region was a remote region of space. This region, located near the Epsilon Canaris system, was in the Alpha Quadrant. There was an asteroid belt in the region, that consisted of approximately 7,000 bodies of sizes running from types A to N. 34 percent of which had atmospheres of types H to M. (TOS: "Metamorphosis")
In the early 22nd century, a non-corporeal lifeform native to this region, known as the Companion, discovered the disabled warp ship of the Human inventor of Earth's warp drive, Zefram Cochrane. The entity brought the ship and its pilot Cochrane safely down to its homeworld, a planetoid in the asteroid belt. The Companion rejuvenated the 87 year old inventor and terraformed the planetoid to sustain Cochrane's life.
In 2267, while transporting the terminally-ill Commissioner Nancy Hedford from Epsilon Canaris III to the USS Enterprise, shuttlecraft Galileo was pulled off course by the Companion and forced to land on its homeworld. Cochrane had told the entity that he would die of loneliness if he didn't have contact with other humans. The Companion merged with Commissioner Hedford moments before her death and Cochrane remained with her on the planetoid. James T. Kirk promised Cochrane that he would not tell Starfleet that they had discovered him or of what had happened on the planetoid. (TOS: "Metamorphosis")
Presumably, the Gamma Canaris region was named after a star named Gamma Canaris.
"The Explored Galaxy"
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. Gamma Canaris N, a planetoid in this region, was located between the Tholian Assembly and Romulus. Both locations were identified in DS9: "The Search, Part II", "Call to Arms" as being located in the Alpha Quadrant. This chart, first seen chronologically in Star Trek VI: The Undiscovered Country, was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game", and DS9: "In the Hands of the Prophets", "Cardassians".