The first time we meet the grown up Elizabeth Swann (played by Keira Knightley) she wakes up from dreaming about her childhood. She is wearing this lovely nightgown which she also wears when she gets kidnapped by Barbossa's crew.
You can see some of the back seams in this picture:
The front looks as though it is full and then gathered together into an empire waist perhaps with some smocking? The fabric appears to be a lightweight linen (or cotton, but I doubt it) with a floral embroidered or woven in pattern.
Here in the back view we can see there are several seams, there are princess seams and also a seam at the waist on the side panels. The Nightgown buttons down the back.
Over her nightgown, Elizabeth wears an embroidered robe, known as a bedgown:
I couldn't find a good view of the back but here you can see how it is full in the back, possibly pleated.
You can see the bedgown is trimmed with green and cream trim around the neckline and runs all the way down the front of the robe on either side. Also notice the sleeves are gathered up almost to the elbow.
Here is a picture of the shoes worn with this costume:
There are notes here on how to make a bedgown.