Hydrogenated vegetable oil is oil from a plant source which has been processed to have more hydrogen than is naturally present. This changes the properties of the fat and makes the oil solid at room temperature. It also lends the oil a longer shelf life.
Unprocessed vegetable oils are liquid at room temperature and not very shelf stable. Adding hydrogen to the oil helps maintain the flavor profile of processed foods for much longer than would be possible otherwise. Hydrogenated vegetable oils are trans fats, meaning that they are unsaturated, have at least one hydrogen atom double bonded to a carbon atom, and have their hydrogen atoms arranged on opposite sides of the molecule. What this means on a medical level is that trans fats raise LDL, or bad cholesterol, and lower HDL, or good cholesterol, levels in the blood.