What is the difference between saturated and unsaturated fatty acids?
Saturated fatty acids are fatty acids with no double bonds and unsaturated fatty acids are fatty acid with one or more double bonds. This is the biggest difference between a saturated and unsaturated fatty acid. 



There is two types of structural configuration for unsaturated fatty acids due to the presence of double bond; cis (kink/bend in fatty acid struture) and trans(No kink/bend in fatty acid struture).

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  cis fatty acid (wikipedia)
  
  A cis configuration means that adjacent hydrogen atoms are on the same side of the double bond. The rigidity of the double bond
  freezes its conformation and, in the case of the cis isomer, causes
  the chain to bend and restricts the conformational freedom of the
  fatty acid. The more double bonds the chain has in the cis
  configuration, the less flexibility it has. When a chain has many cis
  bonds, it becomes quite curved in its most accessible conformations.
  For example, oleic acid, with one double bond, has a "kink" in it,
  whereas linoleic acid, with two double bonds, has a more pronounced
  bend. Alpha-linolenic acid, with three double bonds, favors a hooked
  shape. The effect of this is that, in restricted environments, such as
  when fatty acids are part of a phospholipid in a lipid bilayer, or
  triglycerides in lipid droplets, cis bonds limit the ability of fatty
  acids to be closely packed, and therefore could affect the melting
  temperature of the membrane or of the fat.


Iodine value test is used to determine degree of unsaturation in a unsaturated fatty acids; that is to measure number of double bonds present in a unsaturated fatty acids.

This link will explain the health benifits of saturated and unsaturated fatty acids