In chemical terms, "saturated" has a very specific meaning: it means saturated with hydrogen atoms. In a chemical sense, all fatty acids found in cooking oils are hydrocarbons—molecules consisting of hydrogen and carbon. Fatty acids that contain hydrogen atoms in as many places as possible are fully saturated with hydrogen atoms and simply called "saturated fats." These saturated fats play a predictable role in the cooking properties of an oil. The more saturated an oil, the closer the oil gets to becoming a solid instead of a liquid at room temperature. Highly saturated oils tend to be at least "semi-solid" at room temperature. Placed into the refrigerator—where oils should be stored for long-term use—highly saturated oils become difficult to pour because they take on a more solid texture. Few vegetable oils are highly saturated. This short list primarily includes coconut oil, palm oil, and palm kernel oil. (Most of the highly saturated fats come from animals instead of plants. Examples would include butter, lard, chicken fat, and mutton tallow.)
The opposite is true for unsaturated fats. When highly unsaturated, a plant oil will keep its liquid form even in the refrigerator. Many commonly used cooking oils in the U.S. are chosen for this reason—they stay liquid and are easy to work with, even when refrigerated. In a chemical sense, fats are called "unsaturated" because they have spots that could potentially be filled with hydrogen atoms, but aren't. Since they are not fully saturated with hydrogen atoms, they are called "unsaturated fats." If there is only one spot that doesn't have any hydrogen, the fat is called "monounsaturated." If there is more than one spot, the fat is called "polyunsaturated."