Hyperborea is a common shorthand for the Hyborian Age, a fantasy-mythical period of Earth's history that was invented by Robert E. Howard for his Sword & Sorcery novels. As literally the first officially recognized Sword & Sorcery setting ever invented, it is thusly the most famous of all. Technically speaking, Hyperboria refers to a specific continent in the Hyborian Age, but everybody recognizes Hyperborea more readily because Clark Ashton Smith wrote stories set in his buddy Howard's setting and called them "The Hyperborean Cycle".
The Hyborian Age is set in a dim and murky period in the ancient past, long after the sinking of Atlantis, yet long before the recording of modern history. It has been suggested by some of the writers whom Howard allowed to play in his sandbox that the Hyborian Age takes place at the end of the last ice age - 10,000 BC - and others still that it takes place before the last ice age, around 32,500 BC.
It is a low-magic setting; although mages and monsters certainly exist, magic is rare and requires lengthy rituals fueled by esoteric ingredients, and whilst some aliens and fiends exist, other "monsters" are implied to be merely primeval remnants of animals otherwise extinct.
There have been two Dungeons & Dragons-based gamelines for Conan, a non-D&D Conan RPG, and two RPGs set in the Hyborian Age; the AD&D Retroclone Astonishing Swordsmen & Sorcerers of Hyperborea and the 5e-based Primeval Thule.