What is the chemical difference in saturated and unsaturated fats?

Fat is actually not a compound, it is a mixture of many esterified acids called 'fatty acids'. But it is basically a triglyceride, a triester of Glycerol (C3H5(OH)3) with fatty acids (R):

CH2ORCHOR'CH2OR

The symbol R represents 'aliphatic carboxyl groups' with linear, even numbered, alkane chains.

General formula -C(O)-(CH2)2n-CH3 with n=0,1,2,3....

Some examples of possible fatty acids (esterified, all very common in fat)

Stearate (from stearic acid): -C(O)-(CH2)16-CH3 with n=8, so 'octadecanoate'