Cells divide by a regular and controlled process known as mitosis. This process occurs regularly, but there is typically a period of cell growth where the cell isn't dividing, and the body is able to regulate the number of cells that are being produced.
Abnormal cell growth occurs when certain genetic material in a cell is damaged or altered in some way, by means of UV rays or poisons in cigarettes etc. If the genetic control mechanism by which mitosis is regulated gets damaged, then the cell can begin dividing continually, faster than it is meant to and without control. The body doesn't get rid of these faulty cells because they appear normal and healthy, but they just multiply too quickly.