Final answer:
The yellowish structure is called the corpus luteum and it secretes progesterone during the secretory phase of the menstrual cycle.
Step-by-step explanation:
The yellowish structure that secretes progesterone during the secretory phase of the menstrual cycle is called the corpus luteum. After ovulation, the granulosa and theca cells of the collapsed follicle transform into the corpus luteum, which produces progesterone. Progesterone plays a crucial role in the establishment and maintenance of pregnancy by inhibiting the production of GnRH, FSH, and LH, and by maintaining the endometrium. As the corpus luteum degrades, progesterone levels decline, leading to the sloughing of the stratum functionalis.