i'm going to use progesterone pills as an example to demonstrate how they work.
if you look at a pill cycle, it'll have a 28 day cycle in there. You'll have 21 days of progesterone hormone pills and 7 days of sugar or placebo pills. You menstruate during the 7 placebo pills, and here's why.
The normal cycle is this: when you start your period, your body has entered the estrogen phase of your fertility cycle. This means that your body is heading toward ovulation. once ovulation occurs, your body switches to a progesterone phase. during this phase, your body is expecting that conception has taken place, and when it hasn't, it flips back to estrogen phase, bringing on the menstrual period. Does that make sense?
When you use a progesterone hormone, once you go off of it--the 7 days of placebo--your body 'switches' into estrogen mode to allow the body to release the uterine lining. After the menstrual period is over, you take progesterone pills, such that the body never goes through the process of developing an egg (in the full estrogen phase).
When you start taking birth control pills, you generally start on the first day after you finish your menstrual cycle. This is to prohibit the body from going through the full estrogen phase--preparing an egg for ovulation. This is how hormonal birth control generally works.
When switching pills, if you begin a 'new cycle' of 28 pills 'mid cycle' of your other pills (even if you were off of them for a week, if mensus didn't occur, then it was still in the progesterone phase and didn't 'flip' into menstruation--if often takes a few months to two years for the body to adjust to a normal, ovulatory cycle anyway), then you likely 'skipped' your period and will have it when you hit the placebo pills of the new package.
This is also how some women will simply start a new 'pack' of pills without taking the placebos to avoid mensturating at a certain time. They keep their body high in progesterone to push back the onset of the 'estrogen' phase and thus push back their menstural period until they want to have it. This is also how products like seasonale work.