From Lexicanum

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The Thirst is the term used by Eldar to describe the constant, slow drain of their soul energies by Slaanesh, the Chaos God born from their hedonistic social collapse. Because Slaanesh was created specifically by the Eldar, it has a special connection with their soul energies. Therefore, even though the Eldar exist in the Materium, Slaanesh is still able to slowly feed on their souls, and once an Eldar's soul is separated from its body and returns to the Immaterium, Slaanesh consumes it in its entirety, torturing the fallen Eldar for all eternity.

The Eldar combat The Thirst by encasing their souls in crystals, and adding the souls of their fallen brethren to the Infinity Circuit to prevent them from falling into the hands of Slaanesh.

The Dark Eldar have no such safeguards, and as such they traveled to The Webway, a dimension of their creation in between the Materium and Immaterium, where The Thirst is reduced as much as possible. It does still affect them, however, and so they frequently go on raids to collect slaves from which to harvest replacement soul energy.