How the Biology Works

So while fear is kick-started with the brain reacting to a threat how does it exert it's control over the rest of the body?  The answer is primarily hormones.  When the brain recognizes something frightening enough the pituitary gland starts activating.  From there a cascade of hormones run straight through the body to confront (or run away) from this problems.  These hormones are able to pass through the body so well because they are lipid soluble meaning that they just move through the cell wall will little to no resistance to react their reactors.  An effective method for an almost instantaneous body reaction.  

The body starts moving in the 'fear state' which includes increased blood pressure, blood sugar, and suppression of the immune system.

 All of this jump starts with the creation of glucose dramatically increasing the body's available energy.  This extra energy is what the body uses to fight or flight at an increased rate then what is normally available for a person.  Increased blood flow to the muscles is activated and diverts blood away from non-essential systems.  High blood sugar is the blood moving glucose and fats to gain energy.  Blood clotting is moved into high gear to prevent excessive blood loss in the event of an injury.  Finally, increased muscle tension provides extra speed and strength.

In layman's terms the body is diverting all it's attention away from systems like the immune system that are not immediately needed to save the body an trying to boost the places that can save it.  Really quite smart and thinking in three dimensions.