When it is said that a triglyceride is saturated it means that in its molecule the carbon chain is bound in its maximum capacity to hydrogens, i.e., there are no double or triple bonds between carbons. These saturated molecules are generally solid fats at normal temperature.
Unsaturated triglyceride molecules are those in which there are double or triple bonds between carbons and so they do not accomplish their maximum capacity of hydrogenation. These unsaturated molecules, in general, are oils, liquid at normal temperature.
The terms saturated or unsaturated refer then to the saturation of the carbonic chain by hydrogen atoms.
