Dickinson interestingly uses purple in a number of different contexts in her poetry, and often it is used to refer to the colour of Christ's robes, therefore symbolising his divine rule and imperial majesty. However, Dickinson also uses purple often in her nature poems to describe sunsets and sunrises and the wonders of nature that lie around her. A cursory examination of this poem indicates that this is such a poem, and the use of purple refers to the indescribable beauty of the sunrise as the sun emerges above the horizon and causes a havoc of colours in its wake:
The Sunrise runs for Both--
The East--Her Purple Troth
Keeps with the Hill--
The use of the colour purple therefore is used to symbolise the magnificence of nature and its inherent indescribable beauty, pointing us to the maker and creator of such a scene.
I think in this poem- it stands for the ambiguities of nature. As, purple is often referred to as a 'artificial' colour in the sense that it is not profound in the natural world. Therefore, purple can be acknowledged as a mark for an amazing sight, something different, something not often seen. Which then leads to the idea that something that is not often seen- but which occurs time to time- displays the role of nature in which is to a great extent highlighted as unknown in this poem, as said above.
The ambiguities of nature- or of anything- is what makes something appear so beautiful/remarkable, also.