Actually, no one is 100% sure how birth control works for every woman, every time. Strange, right?
Specifically, birth control works in one of three different ways, depending on many various factors, either by
1) interfering with ovulation,
2) creating an environment in the uterus that is not viable for implantation (ie, thinning the lining of the uterus) and/or
3) creating an environment that makes it difficult for sperm to reach the uterus (thickening the mucus membranes in the cervix, the opening of the uterus).
So, some women still can release an egg and ovulate while taking birth control; others may not.
For all of these reasons, that is why there is a small chance of becoming pregnant in a given year. You can take control of reducing your odds by using your contraception consistently and correctly every time.
The IUD, for example, has an effectiveness rate of 0.3%, better than the 1% you mentioned.
Also, your fear of 20% chance of becoming pregnant over your lifetime is (fortunately) not how the stats work--each year is its own "event" statistically speaking. So, think of this in terms of 0.3% per year odds (depending on the type of contraception you use).
Another thought for you: you can further lessen those chances by "doubling up" on contraception. For instance, if you are using a hormonal method (pill, patch, ring, IUD, etc) than you can also add a barrier method (male condom, female condom, cervical cap, etc). Planned Parenthood has a list of available birth control options, both hormonal and barrier.
Does any of this help?