Final answer:
The ovaries release progesterone through the corpus luteum to enhance the uterine lining for potential pregnancy. If fertilization does not happen, the corpus luteum degrades, and menstruation begins.
Step-by-step explanation:
The structure that releases progesterone to increase the vascularity of the uterine lining is the ovaries. After ovulation, the follicular tissue that released the egg transforms into the corpus luteum. The corpus luteum then begins to secrete progesterone, which is critical in maintaining and enhancing the uterine lining, or endometrium, to prepare it for possible pregnancy. If no pregnancy occurs, the corpus luteum degrades, leading to a decrease in progesterone secretion and the onset of menstruation.