Most birth control pills contain estrogen, which disrupts the female body's hormonal cycle. When present in low levels, estrogen prevents the body from making two different hormones, called follicle-stimulating hormone and luteinizing hormone. Follicle-stimulating hormone helps with the maturation of a follicle in the ovary (for egg release to occur, a follicle has to mature). Luteinizing hormone causes a mature follicle to release an egg (also known as ovulation). As a result, if you stop taking birth control pills mid-pack, the inhibition of these two hormones will disappear, causing them to begin to go through their normal cycle.
According to the Mayo Clinic, there are no additional health risks that come from stopping your birth control in the middle of a pack rather than finishing the pack before birth control cessation. Regardless of when you stop taking birth control pills, you may experience some abnormal vaginal bleeding (also known as spotting), but it should be mild and is not considered a serious health concern. You may run into a problem called post-pill amenorrhea, however. Patients with post-pill amenorrhea may not have their period for many months because their body needs some time to start producing its own hormones again. Although this problem may be frightening, after a few months, the body will begin to start making new hormones and normal periods will resume.
The main thing that happens when a woman stops taking birth control pills in the middle of a pack (or cycle) is that she becomes fertile again. According to the Mayo Clinic, women who stop taking birth control pills typically ovulate two weeks after they stop using the medication. That means that they can become pregnant two weeks after they stop the pill, even if the intercourse happened earlier (because sperm can survive for a limited amount of time in the female reproductive tract). In general, women will have a period six weeks after they stop taking the pills. The period may be abnormally light or heavy, but will return to normal after a few months.