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Triglycerides, fats or oils, are made of three molecules of fatty acids bound to one molecule of glycerol. Hydroxyls of each one of the three fatty acids and each hydrogen of the hydroxyls of the glycerol bind to form three molecules of water that are liberated. 

Glycerol is a linear chain of three carbons; the central carbon is bound to one hydroxyl radical and to one hydrogen and the two other carbons in the extremities are bound to a hydroxyl radical and to two hydrogens. Spatial sides of the hydroxyls are the same.

The main types of lipids are triglycerides (fats and oils), phospholipids, waxes and steroids. 

Fats and oils are hydrophobic molecules, i.e., they are non-polar and insoluble in water. Lipids, in general, are molecules with a large non-polar extension and so they are soluble in non-polar solvents, like benzene, ether and chloroform.

There are some amphipathic lipids, i.e., lipids whose molecules have a hydrophilic portion, like the phospholipids, giving them the property of being dragged by water, and a hydrophobic portion (non-polar).

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.