The Arulin'Holm is a Dalish tool used for carving.
Involvement
In her quest to repair the Eluvian, Merrill asks Hawke to help her borrow the arulin'holm in the possession of her clan, beginning the quest Mirror Image. At the end, Hawke can either give Merrill the arulin'holm or abide by Keeper Marethari's wish to withhold it from her.
Regardless of whether or not she is given the arulin'holm, it will not be enough for Merrill to complete the Eluvian, and she once again asks for Hawke's help in A New Path.