Eating too much saturated fat is one of the major risk factors for heart disease. A diet high in saturated fat causes a soft, waxy substance called cholesterol to build up in the arteries. Too much fat also increases the risk of heart disease because of its high calorie content, which increases the chance of becoming obese (another risk factor for heart disease and some types of cancer).
A large intake of polyunsaturated fat may increase the risk for some types of cancer. Reducing daily fat intake is not a guarantee against developing cancer or heart disease, but it does help reduce the risk factors.