Blackfire Island was a code name that Organization X used to describe their hideout.
To be very specific, although it was not an island, it was located in the southernmost region of Iceland. Iceland itself was surrounded by a large body of water, making it an island country.
Organization X's hideout was a no-man's-land that was surrounded by a range of active volcanoes. The country's government had tried to make use of the fertile volcanic soil many times, but all attempts to repopulate the area were quickly thrown out of the window as soon as another volcanic eruption was in sight.
This was the main reason why the government of Iceland failed to notice the shady movements around the volcanic area for five whole years. By the time they realized that an insidious crime organization already took root in their land, it was already too late.