I have avoided using the common term "Inner World" to describe this concept of personal Headspace because I have many doubts that these spaces are necessarily "inner" at all. In other words they may not be head-space, but real-space. So I am going to refer to this as OtherWorld instead.
In simplest terms, it is the place where insiders go when they are not Fronting. It can be as simple a place as a blank "room" or void, or it can be as complex as an entire world or universe. Such subjective realities may be inner worlds, created specifically as a living-space for those in the system. Or they may be external places, alternate realities, astral dimensions etc, to which members of the system have access. Some members of the system may be Walk-Ins from one of those dimensions.
It may be a place that is totally unique to one system; it may be that only they can interact with it, only they are present in it. Or it may be that this realm is also populated by others who are not part of your own system. It may even be populated with people who are part of other Multiple systems. The evidence that these worlds can be shared is what leads me to refer to them as "Other" rather than "Inner".
It should not be assumed that if someone interacts with an Otherworld then they must be Multiple. I know of several singletons who also have Otherworlds. Likewise some Multiples don't seem to have an Otherworld. (Some paths also have this concept. --Arashi)
The malleability of an Otherworld is also variable. Some systems have total control of the laws of physics in their world. For instance they could suddenly decide that today the sky will be purple and it would instantly be purple. Some have no control beyond that which they would have in a normal earth-like realm - if they suddenly decide they want to live in a big house they must somehow build or buy one. Sometimes the degree of malleability falls somewhere inbetween these examples; perhaps this is a realm where magic is more powerful for instance.
Here is our example of how an Otherworld works for us; DH/DoltagheysWorld
My personal paradigm involves an inner astral, an outer astral and a fuzzy area in between. I think of it as my inner "headspace"; as being like my bedroom. It is essentially mine, with all my stuff, and I have almost complete autonomy over it excepting unusual situations. In this space, I found some one insides (for now, what the does and where she does it is her business). Then, when I leave my bedroom and step into the larger house, I am entering the in- between area. This is where I have a certain amount of autonomy over the space, but so do other people. This is where people might share dreams or interact psychically. When I step out of the house into my neighborhood or go downtown, I'm in the outer astral. No matter the laws of physics, cultural values or accepted realities there, I am in a very collective space in which I have much less say in what goes on, but I have the capability of interacting with all kinds of people. We are sharing the space and can co- create. It's like going to a town meeting and making descisions about how the town is going to funtion. To one degree or another, we make joint descisons about what an outer astral world is going to be like.
Members of my system are from what I consider to be an outer astral world, all but one (so far). You see, there is this place I call Chem World, and it is perceived by all of us as an external world with its own laws of physics, people, things, cultures, relationships and is not inside my head aside from the fact I am able to perceive it. I've gotten jokes about Earth being in the head of one of the members residing on Chem World. They don't care if I dub their place of residence astral or what. They kind of see human/ physical as a less- than- tangible somewhere but believe in it as an external independent world. Members of my sytem have lives, obligations, projects and pursuits all happening independently of what I think and feel (here) back on Chem World. So, in my system of belief, only one other lives *inside* my head, and we're all just constantly hooked into each other despite the fact there is "five degrees of separation" between our respective realities.
Feel free to correct any and all spelling errors or just plain edit. (Minor spelling corrections made. - Del of the Chimaeridae)