Soon she'll throw off her skirts Withering into vestal afterlife,
And now we're back to talking about the flower's short life span, this time in terms of clothing, which is right in line with the personification of the flower as a woman.
To "throw of her skirts," then, would be for her petals to fall off.
As we know, when petals fall off of a flower, the petals themselves wither away, and sometimes the whole plant does too – think of any common annual, like daisies or geraniums. Once they're done flowering, pretty much the whole show is over.
Now, we know that this isn't entirely true for the poppy – after all, there's been all this talk of opium, the seed pod, etc. The exit here is going to be a little more dramatic.
Thus, the flower has an "afterlife" – something, we think, is going to happen here that's not just the plant itself falling to the ground to be replanted next year.
Oh, and for vocab: vestal refers to the mythological virginal priestesses of Vesta, who were important in Roman religion. The word then has come to mean chaste, or pure.