This diagram shows the normal process of ovulation, or egg release. It starts with the primordial follicle, which matures until it becomes a secondary follicle. At that point, the follicle ruptures, or breaks, releasing the egg. It then reseals itself, becoming a corpus luteum, which is broken down into the corpus albicans. This is later reabsorbed into the body.
In a functional ovarian cyst, one of two things has gone wrong with this cycle. Either the follicle never ruptures, or the corpus luteum does not dissolve. In either case, these then fill up with fluid, creating the cyst. Generally, they are broken down by the body within two to three months. Occasionally, they cause problems by bursting or growing large enough to twist the ovary.
Diagram from the National Institutes of Health.