Also referred to as "Soul Crystals."
Empty Soul Gems are referred to as "Creation Containers."
Soul Gems are an item that holds power from a soul, and is the purest form of energy in this world. Madara's undead wizards use them to power many of their spells. With different rituals, a person can use the energy by directly turning it into XP, replenish the energy for a piece of magical equipment, or activate certain special items.
They look like obsidian crystals and are a bit heavy. When placed near a fire, the gem becomes slightly transparent since the power of a soul becomes unstable near fire.
After all of the energy is used, the Soul gem becomes completely transparent and is then called a "Creation Container." Wizards will then use to store their spells. Only those that have MP can activate a stored spell, making it impossible for most Warrior class jobs to use them.
In the game, many wizards from different schools were studying their possible uses. The energy in the gem could be directly converted into XP without any loss, however when converting it into AP you could only get one for every ten XP spent.