A Demesne is much like a Sanctum, except it doesn't exist - at least not in the physical world. It is a ersonal Heaven, a private Hell, and the world of a mage's imagination - his own private Idaho, as the Hollowers say. It also exists in the realm of Dreams, as an islet in the Dreaming, and mages who can find it have a land where they are king and make all the rules.
A mage's rating in Demesne doesn't show how grand or glorious the world of the imagination is, merely how much control the mage has over it. Personal dreams exist there, yes, but so do private terrors and horrible nightmares that embody a mage's darkest fears. Mages with a low rating in desmesne are occasional conscious (albeit sleeping) visitors to the land of their imagination, while those with a high rating are the absolute lords of all they survey, if they so wish it. (A dream lord does not have to appear as a king to rule his own realm, after all.)
This background is particularly useful in combination with a Sanctum with a Shallowing - specifically to the mage's own dream world - and the Body of Light Effect; for in a mage's personal desmesne, the Body of Light is the form that manifests, not the mundane identity. Then again, mages who spend too much time in their Demesne are often viewed with suspicion, because anything can happen in the subconscious - and mages who spend too much time focused inward have a tendency to lose touc with the outside world. Contacts, Allies, and Retainers - particularly sentient dream-entities, or ghosts that visit dreams - are also useful.
Because a Demesne has no physical existence, it's hard for it to interact with the "real world". Still, the mage can sometimes pull bits of useful information or assistance from the dream world. The mage doesn't physically travel to the Demesne (at least, not usually); instead, his consciousness forms a body of sorts (the aforementioned Body of Light) to interact with the locale. Some entities have a dream-form, while others exist physically or solely in dreams. Individuals brought into the mage's dreams with Mind magic also form versions of themselves based on their ideallized personal image. However, once in the mage's Demesne, they are subject to the whims of the mage - at least as far as the mage's tie to dreams allows.
While a character with the Skill:Lucid Dreaming can control dreams to some degree, the mage with a Demesne has dreams with special properties. The mage's dreams literally exst as a spiritual dream realml for most dreamers, this happens only rarely and only when the dreams intersect with the Umbral Dream Realm. As a result, the sleeping mage literally reshapes a portion of the dreaming Umbra to his whims. However, the stuff of dreams is insubstantial and fades with morning light. A mage can't just step into a Demesne, create wondrous effects and artifacts, and expect to take them out with Spirit magic. Such things ultimately have no more substance than the mage's own imagination.
A Demesne can be useful for spiritual travel - mages who project their consciousness into the Dream Realm in this way do no tphysically pass through the Gauntlet and don't suffer the effects of the Avatar Storm. With sufficient power, the mage could then send his projection into other parts of the Umbra. Also, dreams hold significance and overcoming dream-problems and adversaries can prove useful in the struggle for enlightenment or for Seekings.
In game terms, when the mage dreams he creates a pocket Realm tied to the Dream Realm, a small corner where his will reshapes the place without recourse to magic, because it is literally formed of the mage's consciousness. A roll of Perception + Demesne can determine hidden emotional difficulties and sublimated problems; the mage can root out and confront his own internal issues. Wits + Demesne rolls enable the mage to alter the dreamscape; use the magical success chart for guidelines on severity. In theory, a mage could trap someone else's consciousness in his own Demesne, or even shatter it outright - a shattered mind is treated as one that died in a mindscape, while a trapped mind would require careful rescue by clever dream-travelers.
X No special control over your dreams.
* Occasional visitor to the Demesne; at least knows its name,
as well as a few of the perils and virtues.
** Regular sightseer in the dream world. Haven't seen all of it,
but can easily lead a tour.
*** Resident of the Demesne, at least when the dreamer is asleep.
**** Minor Lord of the dream world, commanding great respect
if not absolute obedience from the creatures of the isle.
***** Lord or Lady of the Demesne, with almost absolute knowledge
and control of his or her islet in the Dreaming.