The old woman in the play is a personification of Ireland itself, struggling under the domination of Britain. Thus, for example, when she speaks of her four fields stolen from her, she's actually referring to the four provinces of Ireland.
At the end of the play, we see the rebellion taking shape, with the French landing and the soon-to-be-married Michael being inspired to join the rebellion instead. It is in this context and in this moment that we find the transformation in the old woman into the image of the young and regal girl.
If we hold that the woman is herself a symbol, then it seems to me that this transformation is ultimately tied up to the cause of Irish independence. The old woman represents an ancient country and culture subjugated by Britain. This transformation, shaped within this context of the rebellion, is symbolic of the hope for independence, with this personified Ireland restored to a state of youth and regal dignity.