Rachel is Juliet's sister.
She is ill, and Juliet was secretly treating her with drugs she has stolen from Edmund Burke's laboratory. She revealed that she was miraculously pregnant, apparently after infertility (possible caused by an illness), indicating that the medications Juliet gave worked. ("Not in Portland")
In her room, Rachel keeps an octagon with the yin / yang symbol in its center. This is part of the pattern of the bagua which inspired the DHARMA logos.
Additionally, there is a copy of Carrie on the same bedstand.
Rachel is the name of Jacob's wife in the Book of Genesis. Rachel was disgraced because she had bore no children to Jacob, but her sister and second wife of Jacob, Leah, bore six children (Genesis 30). In the end, God grants Rachel children one of whom is Joseph (essentially restoring her honor). Rachel died in childbirth with her second son Benjamin.