Ghenesh, the infinite plain, is nominally a regency of Amber, though the reality is that the regency was never firmly established. The political issues surrounding the defeat of the Moonriders kept it from ever being firmly established. As such, Amber has a minimal presence in the shadow, and even that is poorly supported.
Ghenesh was more or less unknown to Amber until a few outriders began to appear in the mountains over Arden. Speaking no common language and obviously hostile, these riders were treated as a threat, and wisely so. When the bulk of the massive invading force arrived at the pass over Arden, there was a small force available to stop them. The battle has gone down in the history books as a textbook example of a small defensive force overcoming a large invader. These invaders, the Moonriders, were soundly defeated, and the regency was extracted as part of a weregild.
Corwin was granted the regency for his role in the defense of the pass, and this was seen by many as a move to position Corwin as heir. Many feel that this was the impetus for Eric's final strike against Corwin, and Corwin's disappearance and the subsequent chaos meant that no one stepped in to claim the regency. At first, the obstacles were political - anyone making a play for the regency would mark themselves as likely complicit in Corwin's disappearance and gain Oberon's ire. Over time, the fact that the regency was so poorly developed made it more clear that this was not much of a prize at all. Eric could probably have appointed a regent, but he had other priorities.
Ghenesh is flat, as simple as that. Nothing grows tall, few hills (and no mountains) rise, it is simply a vast expanse of level terrain. Within that limitation is it very diverse - savannah, prairie, tundra, marshland, desert and so on. If there are oceans, they have never been found. Rivers are wide and flat, given to flooding, and there are very few permanent settlements. While there are a few slowly moving tent cities (most famously the Silken Lake) or trading posts, they tend to slowly move over time. The primary exception to this is the Tower of Ribbons, the seat of the regency. It has grown somewhat as a trading post, but it is considered a place of bad luck by those of Ghenesh who know of it.
Virtually every culture in Ghenesh is nomadic, though the specifics vary. Raft-folk travel the rivers and marshes, sail-wagons cross the plains and, of course, the there are the riders. The greatest part of the population ride one manner of beast or another - goats, yaks, battle-giraffes, elephants and so on. The Moonriders are horsemen, and before the war were the greatest of the tribes. They are still mighty, but their strength is not what it was.
The nomadic nature of the people of Ghenesh stems from two principles. The first is the geography - literally boundless horizons have shaped the mindset of the peoples. Building nations is almost pointless when everything is basically flat and goes on forever. The second is more direct. Demons hunt in dreams, and when a man sleeps, they seek him out. They are not good hunters, but they are persistent, and each night that a man spends sleeping in the same place, they grow closer. Thus, it is terribly bad luck for a man to sleep in the same place for more than one night. Now, this may be just superstition, but the men of the regency sleep in rotation, so take that for what you would.
Trade and Resources
The realities of Ghenesh are virtually unknown in Amber. That they are a shadow of horsemen who were beaten by Amber is about the extent of common knowledge, and there is little impetus to change that. Ghenesh is not easy to get to - it's shadowpath is fairly obscure - and the language barrier and lake of infrastructure make any kind of permanent trade arrangement difficult at best. Individual merchants who learn the way and the language can make a decent profit, but large scale ventures have not proven feasible.
Ghenesh lacks metal in any substantial amount. The signature silver swords of the Moonriders are crafted through some secret art, and some are also capable of crafting glass with the durability of wood in small amounts (arrowheads mostly, though the occasional sword or knife can be found). There are no hardwoods to speak of either, though bamboos and other hard grasses serve much of that purpose. Leather and cloth goods are abundant.