[ The Aftermath of Sephiroth ]
Midgar is almost totally destroyed; the survivors have built a city around the outskirts of the old empire, naming it Edge.
Much of the materia upon the Planet has disappeared, absorbed into the Lifestream by the Planet itself to aid its Holy magic.
The Northern Crater is more a destruction zone than ever before; there isn't a single living thing in sight.
The ShinRa Electric Power Company has fallen from its height of power, but has yet to fall completely: although Midgar is gone, their solid power over cities like Junon still remains.
[ Organization Powers/Abilities ]
1. Summoning objects: members of the Organization are able to summon small objects easily out of thin air. The larger the object, the harder it is to summon; something like a car would be the max a single member could do, and that only under intense strain. Also, they can only summon things while -inside- the Twisting Nether, and in order to have the objects with them in the other world, they have to take them out of the Twisting Nether through a portal. Basically, if you can't move/lift it, don't summon it, as it will be no use to you. The only objects that do not fall under these rules are their personal weapons, which are magical in nature and can be summoned anywhere at any time.
2. Creating portals: members of the Organization are able to summon dark portals into the Twisting Nether--not directly to other areas in the world. From the Twisting Nether, they are able to summon portals to anywhere on the Planet, but for them to be able to do that, they -must- have physically visited the location first.
3. Transporting others: members of the Organization are able to transport others through their portals, but this requires much more effort than transporting themselves, and can only be used twice a day* (transport into Twisting Nether, transport out to elsewhere = twice)--and then no more portals may be created at all until the Organization member is rested**.
4. Magic: Organization members (except Xemnas) cannot use materia, as they do not have the required "spirit" (MP) to use materia magic. However, each shard of the Black Materia carries its own element, corresponding with the element of the Organization member that carries it. For example, Axel can use Fire spells, as his shard was of the element of Fire. As for healing, Organization members heal naturally over time at a heightened rate, can use items like Potions to heal themselves, and -do- get healed when hit by healing spells, but they themselves cannot use spells like Cure (as they cannot cast materia magic).
*Day = period of time between long rests.
**Xemnas is able to do this four times a day, as he still holds 2 shards of the Black Materia.
[ The Twisting Nether ]
A smaller, darker world than what we know as the FFVII Planet, the Twisting Nether is a world that is inherently magical in nature and is home to the Organization's castle. The members of the Organization can summon objects while here, and must return to the Nether before teleporting anywhere else. There is no other way in or out of the Twisting Nether besides portals created through the shards of the Black Materia, and should an ordinary person follow an Organization member in, there is no way for them to leave until another member (or someone holding a shard of the Black Materia) lets them out.
The world itself looks much like this.