What is the Luteal phase?

The luteal phase is the second phase of the cycle, and thus after ovulation and before menstruation. This phase ends when the period begins. After ovulation, progesterone is produced from the remains of the follicle that released the egg, the follicle is now called corpus luteum.
Corpus luteum is what produces progesterone, which the body needs to soften the endometrium. This makes it easier for the egg to get fast or when it is time for humans to release endometrium. Increasing the progesterone content in the body also increases the temperature. If the egg is not fertilized, the corpus luteum stops producing progesterone after approx. 12-16 days and it leads to a period.
The luteal phase is between 10-16 days, the average length is 14 days and is usually equally as long in every cycle. If you have a luteal phase defect and your luteal phase is less than 12 days, it may be harder to get pregnant. You can read more about this here.
How the skin is affected during the luteal phase:

Progesterone also stimulates the production of sebum, which is a thick and oily substance that acts a natural skin lubricant. Which can ultimately also cause pores to clog up and be the cause of breakouts.