Substitution is as its name describes; a substitution of one component (I.E. functional group) for another. Let's say you have the formula H3C-CH3 and you perform a substitution reaction involving an OH group. The OH group will replace one of the H's in the molecule giving you an alcohol; H3C-CH2OH.
An addition reaction is when a functional group or atom is added to a molecule. so if you had H2C=CH2 and performed an addition reaction with fluorine, you'd get FH2C-CH2F. So the fluorine gets added to the compound.