Hydrogenation is the process of adding hydrogen to organic compounds. It is done to alkenes.
Vegetable oils have alkenes in them. Alkenes are liquid and spoil easily. People making shortening add hydrogen to the alkene, turning it into an alkane. The alkanes are more solid and stable. A catalyst is used to react the hydrogen with the oil. This makes trans fats, though. Margarine is an example of a hydrogenated spread.
Other things can be hydrogenated, too. Hot nitrogen is reacted with hydrogen under high pressure with a catalyst, usually nickel to make ammonia gas.