One of the enduring mysteries of Final Fantasy VII -- and a point of quite a bit of speculation -- is the nature of the sphere that Cloud sees in his mind while it journeys to battle Sephiroth's form after the destruction of Sephiroth's body (see the sphere here:
Linkage). Sometimes speculated to have been the Promised Land, other times speculated to have been the Cetra's homeworld, and any number of other things, I believe the answer lies in just where it was that AVALANCHE had confronted JENOVA/Sephiroth: The center of the Planet.
To be more specific, AVALANCHE would have been in close proximity to Gaia's core, and I believe that the sphere that Cloud witnessed overhead is
the core itself.
For why I believe this to be so, there is, first, the Lifestream's presence after Cloud has defeated Sephiroth's form, and, second, the very similar sphere seen within Final Fantasy X/X-2's world, Spira, on the Farplane:
The sphere on the Farplane.
Another shot of the sphere.
Recall that the Farplane lay at the center of Spira, and the abundant amount of Spirit Energy (Pyreflies) floating around in there. We know that the lifeforce of the Planet itself resided within the Farplane based on Shinra's analysis of the area in Final Fantasy X-2:
Shinra: Aha...
Yuna: What are you looking at?
Shinra: Farplane data.
Shinra: The more I study it, the more fascinating it gets. There's limitless energy swirling around in there.
Yuna: Limitless energy?
Shinra: The life force that flows through our planet...I think.
Like Spira's core, where Pyreflies (Spirit Energy) freely moved about in close proximity, when Cloud looks up at the sphere above him, there are small orbs of energy floating about.
We find another similarity when looking at the Gaia of Earth in
Final Fantasy: The Spirits Within:
The Gaia. While we can't determine from this shot if the energy below Aki and Gray has a sphere form, based on its depth within the Earth and the nature of density within the Earth, it's safe to assume (as even the metallic core of our own Earth is believed to be a sphere due to density).
While not a very elaborate explanation, I believe that the simplicity of this theory adds to its plausibility, and that it is the most likely of all all possible explanations.