My take on it is the in game one: Atheric remnants of something that had a heavy aether "imprint" on it rendered down into a crystallized form.
As for how they work and why they need to be slotted?
Hammer's take on it, and thus how he designs the mounting slots in weapons/armor for it, is that the materia goes into the bonding lines of the weapon and armor itself, places where the natural flow of battle and magic use would cause the flux of aetheric energy that also makes that spirit bond. Â The materia amplifies that bond, and acts as a amplifier for whatever "type" of bonding energy it's a remnant of.
So someone running around with a weapon with a load of strength materia in it is taking that "bond" you're forming with the weapon, that energy you're pouring into it, and turning it to 11 in the strength facet.
As for how they work and why they need to be slotted?
Hammer's take on it, and thus how he designs the mounting slots in weapons/armor for it, is that the materia goes into the bonding lines of the weapon and armor itself, places where the natural flow of battle and magic use would cause the flux of aetheric energy that also makes that spirit bond. Â The materia amplifies that bond, and acts as a amplifier for whatever "type" of bonding energy it's a remnant of.
So someone running around with a weapon with a load of strength materia in it is taking that "bond" you're forming with the weapon, that energy you're pouring into it, and turning it to 11 in the strength facet.