Mnemosyne is the World of Memory, and is made up entirely of Chaos. As a whole, Mnemosyne is a culmination of all the world's memories. It does not exist as a single, whole world; instead, it shapes itself on a per-person basis. Essentially, Mnemosyne is unique for each person.
Structure
As mentioned, Mnemosyne is more of a personal world than a place with a landscape. The locations and features of the world are entirely dependent on the memories of the individual in the world. However, there is a sort of "hub" that all experience upon entering. It is a void, reminiscent of space, with stars and Chaotic dust drifting by. The individual stands on an invisible floor, and around the hub are doors attached to chunks of land that represent the locations they hold in some form. These doors lead to larger "rooms" that reflect the memories of the individual. These are typically places, but can be multiple places spanning a period of time. Either way, the space is limited in these rooms, and different memories are distinct for a reason. Still, all are connected, but it is unsure in which way. People lost to Mnemosyne usually lose themselves to madness by wandering their memories endlessly.
Note: It is possible to use another individual as an intermediary and enter Mnemosyne with that person's memories. Using this method, it is possible to, say, gain information or witness events in the intermediary's mind. The intermediary must be present in each case, however, or else his or her personal Mnemon will realize that their host is not truly their own.
Inhabitants
One could say that the Mnemon inhabit Mnemosyne. This is true, but as Mnemosyne is not exactly a solidified location, one would be hard-pressed to just go out and find some. The Mnemon we know of are only found on Mundis. In Mnemosyne, they take an entirely different form: memories. Every individual inside Mnemosyne is a Mnemon. Part of the horror of being sent there is watching your precious memories be destroyed as loved ones turn into Mnemon and wreak havoc (this happens as a result of the mind breaking down due to Chaos infection).
Relationship with Other Worlds
Mnemosyne is the source of all Chaos in Mundis, and that will never change. The event of memory creation is the start of this process. From there, the memory naturally heads to Mnemosyne. Whenever that memory is recalled, it returns to the world in the form of Chaos energy. The same is true of Oneiris and dreams.