Emily Dickinson uses the color purple in at least 10 poems that I can think of off the top of my head. In most cases, as in this one, the color refers to royalty.
Purple is the color of royalty, initially because purple cloth was so expensive and hard to come by. Thus, only royalty could own purple clothing.
This poem presents the day as a personified royal woman, clad in a purple petticoat, who is undressing herself. This is significant because typical royal woman would have maids to help with every detail of her life, including dressing and undressing. However, the undressing of the woman parallels the undressing of the day, indicating that the woman may be older and ending her reign as the sun is setting to end a day.
However, the fact that she is wearing a royal color suggests that though her reign is coming to an end, her importance and dignity are not. Similarly, the day, royal in the eyes of Dickinson, is also coming to an end, but its importance and dignity remain forever.