"Did you do it?"
"What did it cost?"
- – A conversation between a vision of Gamora and Thanos, Avengers: Infinity War
Soulstones Spirit stones are psychic crystals used by Craftworld and Exodite Eldar to contain their souls when they die. Dark Eldar don't use spirit stones -- their souls linger in their bodies for a day or so before being lost in the warp, so Dark Eldar who fall in raids can get regenerated and re-animated after an infusion of pain if their bodies are promptly taken to a friendly neighborhood Haemonculus. Eldar Harlequins don't use the stones either, since their laughing god protects them. I'm not sure about Exodites, but I assume Eldar Corsairs use them the same as Craftworld Eldar do.
Among the Eldar, spirit stones are sometimes called "Tears of Isha", after their myth of how the spirit stones came to be. After the god Asuryan separated the Eldar gods from the mortal realm, Isha wept day and night because she missed her children. Vaul, the god of smithing, took pity on her and forged her tears into artifacts that allowed her and Kurnous to speak with the Eldar in secret.
Nowadays, Isha is trapped in Nurgle's garden, and is unable to use the spirit stones to speak with the Eldar, but each Eldar still wears a spirit stone, because when they die, their souls will go into the spirit stones rather than get caught by Slaanesh. Usually, these spirit stones are placed into the craftworld's infinity circuit, which allows the soul within to finally rest, but occasionally the living population of a craftworld is not enough to stand against a threat, and so spiritseers will guide souls out of the infinity circuit and back into their spirit stones, which are then placed into wraithbone constructs like wraithguard or vehicles; the soul inside can then animate the machine and fight once more (though usually not so well as a living operator).
Sometimes, when an Eldar force is routed, many spirit stones are left behind. Because Eldar souls contain much more psychic power than the souls of other species, spirit stones are highly prized by Chaos sorcerers to either crack open and use in rituals, or torture for fun (as Azariah Kyras claimed to be doing with Taldeer's spirit stone). The Eldar are not keen on leaving spirit stones lying around where anyone can get at them, so they will search the whole galaxy for lost spirit stones, and having a spirit stone is an excellent bargaining chip when dealing with the Eldar. Just don't push them too far, or they might decide to kill you and take the spirit stone directly.
The Inquisition appears to be fully aware of the importance of Eldar spirit stones, as in one story where the Grey Knights purged the derelict craftworld of Malan'Tai of a Keeper of Secrets trying to devour the remaining spirit stones inside; the Grey Knights opted to just hand over the surviving ones to an Eldar recovery team, rather than claiming them for study/ransom or trying to give the Eldar a hard time for them, despite the knights losing a few of their own against the KoS.
If the Chaos fluff from various Black Library novels is to be believed, Spirit Stones are pretty much the Chaos Space Marine equivalent of candy, as there are several instances of them being gobbled down as tasty snacks by said Chaos Space Marines. A spirit stone a day keeps the Chaos gods away...