Birth control pills are a small collection of hormones that are absorbed by a woman's body to trick her sex organs into thinking it isn't time to release an egg. This provides protection from pregnancy by making sure that if sperm get past the cervix, which is fairly unlikely then there's no egg to be fertilized in the womb. Like any other medication, it must be absorbed and allowed to take effect. Conditions like sickness, especially with vomiting, can interfere with absorption.
Birth control pills, which are taken orally, take longer to work than birth control patches or injections because the pill must be digested and the hormones absorbed into the blood. The pill must move through the stomach, possibly into the intestine, where it will be absorbed through the lining by the bloodstream. Generally, if a woman takes her birth control pill and vomits within two hours, it's likely that the pill wasn't given enough time to get into her system. Full absorption usually takes between two and three hours.
In order for the birth control pill to work properly, a woman should not miss a dose. Even if a single dosage is missed, it can throw off a woman's entire cycle. If it does occur, she should take other precautions, such as condoms or abstinence until the end of that cycle. Once a woman takes the placebo pills and has her period, a new cycle begins. After the new cycle starts, birth control protection can be considered to be in place.