Can you explain the difference between saturated and unsaturated fatty acids?

The key distinguishing feature between saturated and unsaturated fatty acids is the presence of a double bond. This double bond, present only in unsaturated fatty acids, will mean there are less hydrogen atoms present in the molecule's structure, due to the steric rules governing carbon atoms and their binding (they can only form 4 covalent bonds, with double bonds counting as 2 of those!) As such, the incorporation of double bonds means there are less hydrogen atoms in the fatty acid than there could be, if the double bond were broken open, and hydrogen atoms allowed to bind in its place. As such, the "unsaturated" portion of a fatty acid's name refers to its hydrogen content. If there are fewer hydrogen atoms present that their could be, caused by presence of a double bond, then the fatty acid is unsaturated.

   Unsaturated fatty acids can be either cis or trans, dependant on the nature of the double bond itself. If both of the two remaining hydrogen atoms attached to the carbon atoms involved in the double bond are seen to orientate towards one side of the carbon backbone, then this is a cis-unsaturated fatty acid. However, if the hydrogen atoms orientate to opposing sides of the backbone, it is trans-unsaturated. Saturated and trans-saturated fatty acids will both pack together tightly, due to the repeated and unbroken complimentary nature of the molecular structure the fatty acids maintain. Cis-unsaturated fatty acids will not pack as neatly, due to the stereochemical demand for a kink in the chain of the fatty acid. This is why saturated and trans-unsaturated fats will have higher melting points (due to their more easily condensed structure) while cis-unsaturated fatty acids will generally be oils at room temperature, with lower melting points.