What are Prismatic Stones used for?

The important part is the limit. An Aniimo's core skill takes the upgrade once, which boosts its effectiveness, and that is the end of the line for that creature. A second stone does nothing for it. So every stone you hold is one permanent improvement to one creature, and you choose the creature rather than the amount.

That makes stones a planning item rather than a grinding item. There is no partial progress to chip away at and no reason to hoard past what your team needs, because spreading them across more Aniimo is the only way to spend more. Put one into something you actually intend to keep fielding, since the core skill is the ability you lean on most.

Prismatic energy is a separate resource with a separate faucet. Ecosystem nurturing grants a fixed amount of it, fixed meaning you know what a session is worth before you start and cannot push the number higher by doing more of it.

How it differs from the other upgrade materials

Three materials sit next to each other and none of them substitute for another. Prismatic Stones touch the core skill only. Capability Fruits work on innate potential, granting plus one to each of an Aniimo's two recommended innate potentials, and they can be applied to lower rarity tiers to upgrade those as well. Omnisource Crystals go into Resonance, which pushes an Aniimo's stats past the standard IV maximums.

Read that as skill, potential, and raw stats being three different tracks. A creature with a maxed core skill is still a creature with untouched innate potential. If an Aniimo feels weak after its stone, the problem is one of the other two tracks, not a shortage of stones.

Not settled: Prismatic energy and Prismatic Stones are counted as separate things, and whether nurturing energy is what eventually yields the stones themselves is not settled.