What birth control pills actually do is not quite preventing the 28 day menstrual cycle from beginning, but tricking your body into staying in the luteal phase (days 15-28) the whole time rather than cycling. Since the build up to ovulation happens days 1-14 of the cycle, this keeps you from ovulating which keeps you from getting pregnant.
) shows the changes in hormone levels during the menstrual cycle. The pictures in the top row show the ovaries, with ovulation at day 14. The middle part is the changes in hormone levels and the bottom row is the thickness of the lining of the uterus. Hormonal birth control pills typically are a mix of estrogen and progesterone, though progesterone only pills are also (less) effective.
When you bleed during placebo week, it is technically known as "withdrawl bleeding": the abrupt withdrawl of progesterone is what causes the uterus to shed it's lining. This happens with or without ovulation.
If you miss one pill, there is a chance that you could ovulate, though that chance is very small-- ovulation is unlikely with just on missed pill, which is why the advise is typically to take two pills the next day if you miss one. However, there is a lot of woman-to-woman variation in the days, so in order to be sure to prevent pregnancy pills should not be skipped.