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Shared geometry is a vertex buffer that can be used by multiple submeshes. A submesh can either have its own vertex buffer or use the mesh's shared vertex buffer. If a submesh uses shared geometry, then the submesh's index buffer references the shared geometry of the mesh, otherwise it uses the submesh's vertex buffer. This way you can have different primitive types without duplicating the vertex data.
According to The Ogre Forums:
It is not that common in practice, and in fact, the problems you had with the Maya exporter and the "shared geometry" switch are not unique to your experience — hitting that switch and then trying to use the resulting mesh with, say, an Intel GMA950 chipset will guarantee a crash, as that hardware does not support 32-bit indices (which is one of the unmentioned side-effects of using that option in the Maya exporter — you get 32-bit indices whether you need them or not...and most meshes do not).