Saturated fats are found in animal products and processed foods, such as meats, dairy products, chips, and pastries. The chemical structure of a saturated fat is fully saturated with hydrogen atoms, and does not contain double bonds between carbon atoms. Saturated fats are not heart healthy, since they are most known for raising your LDL cholesterol (bad cholesterol).
Unsaturated fats, on the other hand, are found foods such as nuts, avocados, and olives. They are liquid at room temperature and differ from saturated fats in that their chemical structure contains double bonds. Additionally, studies have shown that unsaturated fats are also heart-healthy fats - they have the ability to lower LDL cholesterol and raise HDL cholesterol ("good" cholesterol).
So, if you are trying to follow a cholesterol-lowering diet, eating unsaturated fats should not raise your cholesterol levels further. However, you should try to avoid foods high in saturated fats.
Sources:
Rolfes SR, Whitney E. Understanding Nutrition, 3rd ed 2005.

