Giving the Fire Keeper the Fire Keeper Soul lets her cure your Dark Sigils, which removes Hollowing for a soul cost. If you do that, you can stop the Hollowing progression, but it can also lock you out of the Usurpation of Fire ending if you were aiming for it.

What it does

  • She gains the ability to heal Dark Sigils.
  • You can pay souls to remove each Dark Sigil.
  • Your Hollowing stops increasing once the sigils are cured.

Why it matters

  • Removing the Dark Sigils changes your ending path.
  • If you want the Yuria/Usurpation of Fire route, you generally should not cure the sigils.
  • If you are not doing that ending, giving her the soul is usually useful because it cleans up Hollowing.

Simple version

Give the soul if you want to cure Hollowing.
Hold onto it if you want to keep the Usurpation of Fire route open.

TL;DR: It unlocks Dark Sigil healing, but curing them can affect your ending choice.