In adulthood, new cells are produced only to replace those that die of old age, injury or disease. As mentioned, no more egg cells are ever produced after womb life, however other ovarian cells are. Normally, division of cells is under very tight control. The genes themselves are made up of DNA, the master genetic code material. If the genes are damaged, say by chemicals or radiation, the control over cell division may be lost in one particular cell.
Ovarian cancer starts in a single cell.
That cell starts dividing haphazardly, making millions and billions of copies of itself. It takes up the nourishment needed by other cells, depriving them so the cancer can continue to grow. A tumor simply means a swelling, it can be caused by inflammation or infection. It is this capacity for spread that makes cancer so dangerous. In younger women, most ovarian tumors are benign cysts and are not dangerous.