This poem concerns one of Emily Dickinson's favourite themes in her writing, which is that of death. The poem concerns the way in which an acquaintance or friend met her death with honour and dignity, and, if you look at the last verse, deals with how she has exchanged her reality on this earth for a much greater reality in the kingdom of her heavenly father. However, the reference to the colour purple that your question refers to can be found in the first stanza:
She bore it till the simple veins
Traced azure on her hand—
Til pleading, round her quiet eyes
The purple Crayons stand.
Normally, purple is a colour that we can relate to a position of power, authority and dignity. For example, elsewhere in Dickinson's poetry, the colour purple is used to describe the colour of the robes of Jesus. However, based on the context, here we can say that it is being used in a very different fashion, as the "purple Crayons" refer to the veins of the woman that is dying and how, as her condition worsened, the veins became more pronounced and the colour became darker. The metaphor is used to compare those veins to marks on her face made by a purple crayon. The colour here therefore is used to reflect the worsening condition of the woman, and signal her approaching death.