How does chemotherapy work to treat cancer?

Slows down the multiplication of quickly dividing cells, like cells.
Cancer is caused when multiple genes stop regulating cell division and cell differentiation. What this leads to is the unchecked multiplication of cells, which can build up into tumors. Some tumors are benign, some are malignant. A benign tumor will stay in the same place, however, a malignant tumor is a sign of cancer and will move about.
Since cancer is the rapid, unrestrained division of cells, chemotherapy is the opposite process. It stops or slows down the division of all cells that divide quickly, however, this can harm healthy cells that divide quickly, like cells that cause hair to grow.