Having unprotected sex at any time immediately prior to your period can result in conception and pregnancy. Your period is the point in your cycle when the uterine lining is flushed away at the completion of a fertility cycle that doesn't result in pregnancy. This cycle is the reason why, according to About.com, you are at your peak fertility during the ovulation phase immediately prior to your period.
Approximately every 28 days, a healthy woman's body releases one of the 400,000 eggs in her ovaries. This egg travels down the fallopian tube to the uterus over the course of about two days. If the egg encounters sperm during that time, conception can occur. This part of the cycle is known as ovulation, and About.com cites it as the six-day period in the cycle when conception is most likely to take place.
Pregnancy proceeds by stages and is only accomplished once the fertilized egg implants in the mother's uterine lining. This lining has been building up in anticipation of receiving the embryo and will be flushed away if implantation doesn't occur. From this model, it's clear that the one to six days immediately preceding the visible symptoms of your period are your most fertile time.