Progesterone increases in the second half of a woman's cycle to prepare the body for pregnancy, for implantation of the fetus. Without progesterone, pregnancy is aborted. Progesterone also offsets the proliferative effect of E on the uterus, thereby preventing uterine/endometrial cancer.
One needs not take it cyclically as there is really no apparent benefit. But, if your doctor says you should, then do as instructed and ask perhaps why he/she prefers this approach.
Progesterone has a calming/sedative effect that results from the effect of one of its metabolites, allopregnanolone, especially when taken orally, and with food (especially fatty). It helps improve sleep in some and reduces anxiety. This is what you are experiencing. Pretty cool, right? Best to take it before bedtime but I also take it during the day to keep levels steady as half-life is quite short.