That this head is veiled indicates that the subject was a married woman. She may have originally been part of a family funerary scene. As the proper right fold of her veil appears to extend outwards, she likely held the edge of the drapery at shoulder height with her right hand, a gesture associated with brides and married women. Grossman (Greek Funerary Sculpture, p. 7) suggests this pose originated with the ritual unveiling of the bride in a Greek wedding (anakalypteria).
For a standing draped female in mourning holding her veil, now in the Louvre, see no. 213 in Hamiaux, Les Sculptures Grecques. For a seated example in relief on a marble grave stele, now in the Getty Villa, see no. 7 in Grossman, op. cit.