Most systems of the pill have you take hormones for three weeks, then either no pills or sugar pills for a week. This causes a bleeding similar to menstruation
For health reasons, this period of bleeding is not necessary. It was 'invented' because the people who invented the pill thought women would prefer the bleeding period, which makes it seem like you have a normal menstrual cycle. When you prefer not to experience this, because you're on holiday for example, you can opt to just keep on taking the pills and skip the bleeding.
Recent research suggests that when you never interrupt your taking of the pill, this may decrease your chance of pregnancy. There are two reasons for this: first, the steady flow of hormones means there's less chance of ovulation. Second, because there is no week in which you don't take any pills, there's less chance that you forget to take them when you need to again. When you don't observe the "stop week", there is a chance you get a bleeding anyway after a while; you could choose to stop taking the pill for 7 days if this happens.
Important! The above is not valid for all birth control pills. Ask your doctor to be sure if you want to try this!
I have tried this myself. The results were not very positive: in stead of a bleeding period of a few days, I got a trickle that lasted for weeks. Not much of an improvement...
Source: PhD thesis "Residual Ovarian Activity During Oral Contraception" by gynecologist Arne van Heusden, Erasmus Univeristy, Rotterdam