"He slunk along alleys and shadowed plazas until he came to the district which was his destination -- the Maze. Along its labyrinthian ways he went with the certainty of familiarity. It was indeed a maze of black alleys and enclosed courts and devious ways; of furtive sounds, and stenches." -- Robert E. Howard: "Rogues in the House"
One of the lesser Hyborian kingdoms (or perhaps a confederacy), comprised of loosely allied city-states and presumed to be mostly mountainous. It lay south of Brythunia and Nemedia, west of Zamora, east of Ophir, and north of Koth.
The western reaches contain rank after rank of forested ridges, extending to the jagged wall of the Karpash Mountains. The Road of Kings, a major trade route, passed through central Corinthia.
Corinthia apparently had a separate identity as early as the florescence of Acheron. It was subject to the latter, then "gained its independence" with the fall of the ancient empire to the Hyborians.
Some time during the 3000 years that followed, it came under the growing hegemony of the Hyborians. The economy of Corinthia may have been both pastoral and agricultural, with specialized small industries in the city-states.
References: Hyborian Age I-II, Rogues in the House, Shadows in the Moonlight, Jewels of Gwahlur, Conan the Great.