Eidolons are beasts that dwell in Valhalla. L'Cie chosen by Etro are pitted against Eidolons in a trial by combat. Those who emerge triumphant receive a crystal called 'eidolith,' which they may use to summon the beast to fight at their side.Gerhilde's Blossom Fragment in Final Fantasy XIII-2.
Eidolith is a type of crystal in Final Fantasy XIII and Final Fantasy XIII-2 granted to l'Cie. After defeating an Eidolon sent by the goddess Etro, the person's eidolith allows them to summon said Eidolon. Each person's eidolith is of unique color and shape, and is the basis of their Crystarium system for stat development.
Lightning and her new allies of circumstance are chosen by the fal'Cie Anima and branded by the god Pulse as l'Cie. The party descends into an alternate realm where a dark figure ( identified as the god Pulse) emerges out of a crystal and strikes the party somewhere on their bodies; where "touched" by the god, the l'Cie have the brand of l'Cie, but furthermore, this act appears to grant the l'Cie their eidoliths. This allows them to use magic and learn new abilities via the Crystarium, whose grid extends out of the eidolith, making them far more powerful than regular humans. Whenever the l'Cie cast magic, they channel it from the eidolith in their body.
The eidoliths are not obtained as key items in the inventory before the l'Cie has tamed their Eidolon. The item descriptions describe eidoliths as crystals that house the souls of the l'Cie's respective Eidolons. It appears that even though the l'Cie possess their crystals ever since having become l'Cie, they are not "aware" of their exact existence before having summoned their Eidolon for the first time. Progressing on their quest the party's Crystaria grow, which also affects their Eidolons' strength.
During times of conflict the goddess sends Eidolons to the l'Cie's aid and the l'Cie summon their Eidolons by manifesting the image of their eidolith and shattering it. For example, after the party's airship is destroyed and they are sent falling through the air toward Gran Pulse, Fang manifests her eidolith and throws it in the air; when Lightning shoots it with her weapon, Bahamut is summoned.
Even people who have never been made l'Cie can progress through the Crystarium and thus use magic due to the soil of the earth having absorbed crystal dust on the Day of Ragnarok. The Crystarium for the party members in Final Fantasy XIII-2 looks different than it did in Final Fantasy XIII, and an eidolith is no longer the origin of the system.
The notable eidolith is that of Caius Ballad, which he keeps in his sword, as opposed to it being implanted into his body. Caius used to be a l'Cie whom goddess Etro saved, and can perform incarnate summoning to transform into Chaos Bahamut.
Eidoliths are individual to the summoner rather than the Eidolon, as Lightning summons both Odin and Bahamut with her rose-shaped eidolith.
Lightning's eidolith appeared to her after Odin was defeated during the Final Fantasy XIII collaboration event.
Serah's crystal tear
Serah's crystal that she sheds when she enters crystal stasis resembles the party's eidoliths, and is carried by her fiancé Snow for most of Final Fantasy XIII, who believes he can speak to Serah through it. In Final Fantasy XIII -Episode i-, it is revealed that Serah could indeed see the party's journey through the crystal, implying it housed part of her essence similar to the essence of the Eidolons contained in the eidoliths. In Final Fantasy XIII-2 and Lightning Returns: Final Fantasy XIII, the crystal tear appears alongside the party's eidoliths as an adornment.
- Final Fantasy XIII-2, "Omega Brand" Fragment entry