Fats as Natural Esters
Oils and fats are esters of propane-1,2,3-triol (glycerol). [Seen below]
Each alcohol group can be esterified. When one group is esterified, the product is a monoglyceride; two groups means it is a diglyceride and all three groups means that it is a triglyceride.
Saturation
The carboxylic acids from the hydrolysis of natural fats and acids typically have long carbon chains. Moreover, they usually have an even number of carbons in an unbranched chain.
The concept of saturation is a very similiar concept to that covered in the AS syllabus; a saturated carboxylic acid contains no C=C bonds in the carbon chain, while a monounsaturated acid has one C=C bond in the chain, while an acid with multiple C=C bonds in the chain is described as being polyunsaturated.
The presence of a C=C double bond of course gives rise to cis-trans isomers due to the inability of the bond to twist [ I have had a long arguement with my chemistry teacher, Mr. Saddler, over whether the C=C bond is incapable of rotation or twisting. I personally come down on the side of twisting, as rotation would imply it is in a fixed position in space relative to a pivot position, whereas twisting implies the movement would be within the bond itself, which is the sort of movement the double bond would restrict.].
Notation which may prove useful is the tendency of scientists - among whom you may or may not count yourself among - to shorten the names of such an acid to CX, Y (Z1, Z2 ...ZY), where X is the total number of carbons in the chain, Y is the number of C=C bonds and Zn is the number of the first carbon in each bond when labelling in the standard manner, from the functional group.