What effects does having the Armored armor type have on a unit aside from taking the appropriate extra damage from weapons that deal extra armored damage? I.E. do normal attacks do reduced damage or something?
There is no benefit to having Armored as your armor type, only drawbacks.
Because most units only have a single armor type (of Armored vs Light), it is often considered a benefit in not be vulnerable to light. However, there is nothing in Starcraft which stipulates that a unit must have a single armor type, and it is possible (through the galaxy editor) to create units which are both Armored and Light.
It is worth noting that Armored is not your only type on most units; many units also have types of
As a rule of thumb the Armored vs Light, is usually the drawback and the Mechanical vs Biological the benefit. There are two notable exceptions to this rule: Archons do bonus damage to Biological and Ghosts can use the ability
tzenes's answer has all the specific details you'd want, but the general answer is that none of the unit-descriptor tags like 'Armored' or 'Massive' do anything on their own. They are just descriptive tags that other units and abilities will play off of.
For example being 'Armored' by itself does not do anything, but there are various attacks that do more or less damage to armored units.