What happens between days 7-13 of the menstrual cycle?

Typically this would be the follicular phase.

During this phase folicle stimulating hormone is produced which causes some of the ovums within the ovary start to mature ready for ovulation (typically on day 14-16 of an average menstrual cycle of 28 days). It's also during this time that the woman's body would produce fertile quality cervical mucus. The cervical opening is normally plugged-up with thick mucus, approaching ovulation the mucus softens and changes so it opens the cervical opening and drips into the vaginal canal, this allows sperm to climb up through the cervix and this mucus also helps keep sperm alive in the acidic pH of the vagina so it can live up to 7 days.