The word saturated simply means that something is completely full and cannot take any more. In this specific case, every single carbon atom has formed four single bonds with its neighbors. There is no empty space left for any additional hydrogen atoms to join the molecular structure.
This is very different from unsaturated molecules, which have double bonds that can easily pop open to grab more atoms. Saturated hydrocarbons are officially known as alkanes in the world of organic chemistry. A common student misconception is that these molecules are highly reactive and dangerous.
While they certainly burn easily in oxygen, they are actually very stable and lazy at room temperature. They strongly resist reacting with harsh acids, strong bases, or highly active metals. You usually must use extreme heat, special catalysts, or bright ultraviolet light to force them to react.
This impressive chemical stability comes from their strong and evenly shared single bonds. You interact with saturated hydrocarbons every single day of your life. They make up the vast majority of natural gas, gasoline, heavy motor oils, and candle wax.